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Business Math – Chapter 3 Review Questions and Answers

 

Note from the Editor:

This set of worked solutions is based on an earlier version of this text, and might not be exactly the same.  The formatting also didn’t perfectly sync over, so please email me at amy_goldlist@bcit.ca with any corrections needed (ie, incorrect math.) I’ll update the formatting soon – AG.

 

Business Math – Chapter 3 Review Questions and Answers

Do not forget to draw your time diagrams!

 

Do not forget to draw your time diagrams!

Question 1

For each principal, rate and time given below, compute the interest:

a. $2,500 at 14.2% for 1.5 years.

b. $3,200 at 8.75% for 16 months.

c. $8,300 at 11.2% for 160 days.

d. $800 at 13.6% for 212 days.

I = PRT
Principal Rate Time
1 a. $2,500 at 14.2% for 1.5 years at 14.2% for 1.5 years
2500 0.142 1.5 I = $532.50
b. $3,200 at 8.75% for 16 months $3,200 at 8.75% for 16 months
3200 0.0875 16/12 I = $373.33
c. $8,300 at 11.2% for 160 days $8,300 at 11.2% for 160 days
8300 0.112 160/365 I = $407.50
d. $800 at 13.6% for 212 days $800 at 13.6% for 212 days
800 0.136 212/365 I = $63.19

Question 2

Calculate the interest for each of the following loans:

a. $850 at 11.5% from June 14, 2002, to October 19, 2002.

b. $2,800 at 11.25% from September 9, 1999, to March 19, 2000.

c. $4,100 at 7.5% from July 15, 2002, to September 6, 2002.

Principal Rate Time
2 a. $850 at 11.5% from June 14, 2002, to October 19, 2002 $850 at 11.5% from June 14, 2002, to October 19, 2002 $850 at 11.5% from June 14, 2002, to October 19, 2002 $850 at 11.5% from June 14, 2002, to October 19, 2002
850 0.115 127 I = $34.01
b. $2,800 at 11.25% from September 9, 1999, to March 19, 2000 $2,800 at 11.25% from September 9, 1999, to March 19, 2000 $2,800 at 11.25% from September 9, 1999, to March 19, 2000 $2,800 at 11.25% from September 9, 1999, to March 19, 2000 $2,800 at 11.25% from September 9, 1999, to March 19, 2000
2800 0.1125 192 I = $165.70
c. $4,100 at 7.5% from July 15, 2002, to September 6, 2002 $4,100 at 7.5% from July 15, 2002, to September 6, 2002 $4,100 at 7.5% from July 15, 2002, to September 6, 2002 $4,100 at 7.5% from July 15, 2002, to September 6, 2002
4100 0.075 53 I = $44.65

Question 3

Complete each row in the following table:

Interest Principal Rate Time
a. ? $2,800 12% 210 days
b. $461.25 $6,000 ? 8 months
c. $ 54.00 $1,440 11.5% ? days
d. $ 81.30 ? 6.25% 205 days
3 Interest Principal Rate Time
I = PRT
a. ? $2,800.00 12% 210 days
$2,800.00 0.12 210/365
$193.32
b. $461.25 $6,000.00 ? 8 months
= I x 12/time = I x 12/time
691.875
11.53%
c. $54.00 $1,440.00 11.50% ? Days
T =I/(PxR)
54/ (1440*0.115) 54/ (1440*0.115)
0.326086957 of a year 0.326086957 of a year
119.02 days or 120 days
d. $81.30 ? 6.25% 205 days
P = I/(RxT)
81.3/(0.0625 *205/365) 81.3/(0.0625 *205/365)
$2,316.06

Question 4

Find the interest rate which will pay $36.40 interest on a principal of $2,140 borrowed for 69 days.

4 Interest Principal Rate Time
$ 36.40 $ 2,140.00 ? 69 days
R= 36.4 / (2140 x 69/365) 36.4 / (2140 x 69/365)
8.997% or 9.0%
R = 9%

5 If a loan of $1,900 borrowed from October 22, 2001 to December 17, 2001 resulted in $33.85 interest, what was the simple interest rate charged?

5 Interest Principal Rate Time
33.85 $ 1,900.00 ? Oct 22, 2001 to Dec 13, 2001 Oct 22, 2001 to Dec 13, 2001 Oct 22, 2001 to Dec 13, 2001
56 days = 0.1534 years 0.1534 years
R= I / (P x T)
33.85 / (1900 x 0.1534) 33.85 / (1900 x 0.1534)
R = 11.61%

Question 6

What principal will earn $95.20 if borrowed at 13.5% for 4 months?

6 Interest Principal Rate Time
$ 95.20 ? 13.50% 4 months = 1/3 years
P = I/(RxT)
95.2/(0.135 x 1/3) 95.2/(0.135 x 1/3)
P = $2,115.55

Question 7

How many days will it take for a principal of $19,200 to earn $650.00 interest at 10%?

Interest Principal Rate Time
7 $650 $19,200 10% ? Days
T = I /(PxR)
650/(19200 x0.1)
0.3385 years
123.568 days
T = 124 days

Question 8

What is the future value of $1,680 over 260 days at 11.25%?

Interest Principal Rate Time
8 ? 1680 11.25% 260 days
=260/365
I =? PxRxT
136.63
FV = P + I 1680 + 136.63
FV = $ 1,814.63

Question 9

Find the principal and the interest if a loan at 12.5% for 9 months is completely paid off by the payment of $1,732.22 at the end of the 9 months.

Interest Principal Rate Time
9 ? ? 12.50% 9 months
P +I = PRT + P
P + I = $1,732.22 P [(RT) +1]
P (1+(RT))
P (1 +(0.125) x (3/4)) P (1 +(0.125) x (3/4))
P (1+ 0.09375) P (1+ 0.09375)
1732.22 1.09375 P
1732.22/1.09375 1732.22/1.09375 = P
$1,583.74 = P
I= (P+I) – P
I = 1732.22 – 1583.74 1732.22 – 1583.74
148.48
P= $1,583.74 I = $148.48

Question 10

If 9 months interest at 8.725% is $186.20, what principal was borrowed?

10 Interest Principal Rate Time
$186.20 ? 8.725% 9 months
3/4 year
P= I/ ( RT) 186.2/ (0.08725 x0.75) 186.2/ (0.08725 x0.75)
2845.463228
P = $2,845.46

Question 11

A loan at 9% was repaid by a payment of $3,710 of which $307.40 was interest. What was the length of time (in days) of the loan?

11 Interest Principal Rate Time
$307.40 ? 9% ? Days
P + I = $3,710
P = 3710 – 307.4
$ 3,402.60
T = I / (PR)
T= 307.4/(3402.6 x 0.09) 307.4/(3402.6 x 0.09)
1.003807546 years
366.3897542
T = 367 days

Question 12

If the future value of a loan for 222 days at 11.75% was$937.72, what was the principal of the loan?

12 Interest Principal Rate Time
? ? 11.75% 222 days
P + I = $937.72 P +I = PRT + P
P [(RT) +1]
P (1+(RT))
937.72 = P (1 +(0.1175 x 222/365)) P (1 +(0.1175 x 222/365))
937.72 = P x 1.07146575
937.72 / 1.07146575 937.72 / 1.07146575 = P
875.174965 = P
P = $875.17

Question 13

A loan is to be repaid in 9 months by a payment of $1,300. If interest is allowed at 13.15%, what is the present value of the loan?

13 Interest Principal Rate Time
? ? 13.15% 9 months
P + I = $1,300.00 P +I = PRT + P
P [(RT) +1]
P (1+RT)
1300 = P (1 + (0.1315 x 0.75)) P (1 + (0.1315 x 0.75))
1300 = P 1.098625
1300 / 1.098625 1300 / 1.098625 = P
1183.2973 = P
P = $1,183.30

Question 14

Payments of $5,000 due in 3 months and $6,000 due in 9 months are to be paid off with interest allowed at 13%. How much would be required to pay off the loan today? (Use today as the focal date.)

14 Interest Principal Rate Time P + I
? ? 13% 3 months $5,000
P = (P +I)/ ( 1 + ( RT)
5000 /( 1 + (0.13 x 0.25)) 5000 /( 1 + (0.13 x 0.25))
P = 4842.615012 P1 = $4,842.62
Interest Principal Rate Time P + I
13% 9 months $6,000
P = (P +I)/ ( 1 + ( RT)) (P +I)/ ( 1 + ( RT))
6000/(1 +(0.13 x 0.75) 6000/(1 +(0.13 x 0.75)
5466.970387 P2 = $ 5,466.97
Total Payment Total Payment $10,309.59

Question 15

LH should have paid a loan company $2,700 3 months ago and should also pay $1,900 today. He agrees to pay $2,500 in 2 months and the rest in 6 months, and agrees to include interest at 11%. What would be the size of his final payment? Use 6 months as the focal date.

15 Interest Principal Rate Time
$2,700 11% 9 months P1 = 2,700.00
I = PRT 2700 x 0.11 x 0.75 2700 x 0.11 x 0.75
222.75 I = 222.75
2,922.75
Interest Principal Rate Time
$1,900.00 11% 6 months 1,900.00
I = PRT 1900 x 0.11 x 0.5 1900 x 0.11 x 0.5
104.5 104.50
4,927.25
Interest Principal Rate Time
$2,500 11% 4 months – 2,500.00
I = PRT – 91.67
2500 x 0.11 x 1/3
91.66666667 Final Payment 2,335.58

Question 16

AW borrowed $9,000 on January 30, 2002 and agreed to pay 14% simple interest on the balance outstanding at any time. He paid $5,000 on March 9, 2002 and $2,500 on May 25, 2002. How much will he have to pay on June 30, 2002 in order to pay off the debt? Use June 30, 2002 as the focal date.

16 Interest Principal Rate Time
$9,000 14% Jan 30 Jun 30 $9,000
151 days
I = 9000 x 0.14 x 151/365
521.260274 $521.26
Interest Principal Rate Time
$5,000 14% Mar 9 Jun 30 -5000.00
113 days
I = 5000 x 0.14 x 113/365
216.7123288 -216.71
Interest Principal Rate Time
$2,500 14% May 25 Jun 30 -2500.00
36 days
I = 2500 x 0.14 x 36/365
34.52054795 -34.52
June payment $1,770.03

Question 17

Debts of $8,000 due 8 months ago and $3,000 due in 4 months are to be paid off today with interest at 12%. Use today as a focal date and find the size of the payment.

17 Interest Principal Rate Time
$8,000 12% 8 months $8,000
I = 8000 x 0.12 x 2/3
640 $640
Interest Principal Rate Time P + I
12% 4 m future $3,000 $3,000
P = (P +I)/ ( 1 + ( RT))
3000 / (1 + (0.12 x 1/3)) 3000 / (1 + (0.12 x 1/3))
2884.615385
-115.38
I = (P + I) – P
3000 – 2884.62 Payment of $11,524.62
115.38

Question 18

$5,000 due today is to be paid instead by payments of $2,000 in 4 months and the balance in 9 months. Find the size of the last payment if interest is at 9% and the focal date is today.

18 Interest Principal Rate Time
$5,000 9% 9 months 5000
Interest Principal Rate Time P + I
9% 4 m 2000
P = (P +I)/ ( 1 + ( RT))
2000/ (1 + (0.09 x 1/3)) 2000/ (1 + (0.09 x 1/3))
1941.747573
$1,941.75 – 1,941.75
$ 3,058.25
Interest Principal Rate Time
$3,058.25 9% 9 months
I = 3058.25 x 0.09 x 3/4
206.431875 206.43
Final Payment in 9 months Final Payment in 9 months $ 3,264.68

Question 19

Two payments of $1,200 each were due 30 and 60 days ago. They are to be paid off by two equal payments, one in 60 days and one in 90 days. If the focal date is 90 days from today and interest is at 12%, find the size of the payments.

19 Interest Principal Rate Time
$1,200 12% 120 days (30 + 90) 1200
I = 1200 x 0.12 x120/365
$ 47.34 47.34
$1,200 12% 150 days (60 + 90) 1200
1200 x 0.12 x150/365
$ 59.18 $ 59.18
2,506.52
2506.52 = P1 + P2 P1 = FV/(1+rt)
P1 = (x/(1+0.12*30/365) P1 = (x/(1+0.12*30/365)
P1 = 0.009863x P1 = 0.009863x
2506.52 = 0.009863x + x
2506.52 = 2.009863x
2506.52/2.009863 = x = 1,247.11
Each payment should be $1,247.11 Each payment should be $1,247.11

Question 20

Find the present values of the following payments if money is worth 8%:

$2,800 to be paid in 60 days.

$950 to be paid in 120 days.

$56,000 to be paid in 1 year.

20 Interest Principal Rate Time P + I
a. 8% 60 days $2,800
P = (P +I)/ ( 1 + ( RT))
2800 / ((1 +(0.08 x 60/365)) 2800 / ((1 +(0.08 x 60/365))
2763.65603
P = $2,763.66
Interest Principal Rate Time P + I
b. 8% 120 days $950
P = (P +I)/ ( 1 + ( RT))
950 /(1 +(0.08 x 120/365)) 950 /(1 +(0.08 x 120/365))
925.654031
P = $925.65
Interest Principal Rate Time P + I
c. 8% 1 year $56,000
P = (P +I)/ ( 1 + ( RT))
56000/ (1+(0.08×1)) 51851.85185
P = $51,851.85

Question 21

You invest $1,000 for 4 years at 8% simple interest. How much interest will you earn?

21 Interest Principal Rate Time
$1,000 8% 4 years
I = PRT
1000 x 0.08 x 4
I = $ 320.00

Question 22

You invest $6,000 for 2.5 years at 9% simple interest. How much interest will you earn?

22 Interest Principal Rate Time
$6,000 9% 2.5 years
I = PRT
6000 x 0.09 x 2.5
I = $ 1,350.00

Question 23

$6,000 earns $180 in interest when invested for 30 months. What simple rate of interest is being paid?

23 Interest Principal Rate Time
$180 $6,000 30 months
2.5 years
R= I/(PT)
180 / (6000 x 2.5)
0.012
R= 1.20%

Question 24

A $1,000 savings bond earns $600 in interest over the 12 years of the investment. What simple rate of interest is being paid?

24 Interest Principal Rate Time
$600 $1,000 12 years
R= I/(PT)
600 / (1000 x 12)
0.05
R= 5.00%

Question 25

You would like to earn $1,000 in interest each year. If the interest rate is 6% simple how much money should you invest?

25 Interest Principal Rate Time
$1,000 6% 1 year
P= I / (RT)
1000 / (0.06 x 1)
16666.66667
P = $16,666.67

Question 26

You take a 3-year loan and repay the loan and $800 in interest. How much did you borrow if the interest rate was 10% simple?

26 Interest Principal Rate Time
$800 10% 3 years
P= I / (RT)
800 / (0.1 x 3)
2,666.67
P = $2,666.67

Question 27

You would like to save for a vacation in Edmonton. You need $4,000 for your dream vacation. You deposit $3,000 in an account that pays 8% simple. How many months will it take you to save for your vacation if you make no other deposits?

27 Interest Principal Rate Time
$1,000 $3,000 8% ?
T = I / PR
1000 / (3000 x 0.08)
4.166666667
4.17 years
T= 50 months

Question 28

You invest $1,000 for 18 months at 8% simple interest. How much interest will you earn?

28 Interest Principal Rate Time
? $1,000 8% 18 months
1.5 years
I = PRT
1000 x 0.08 x 1.5
I = $ 120.00

Question 29

You take out a loan for 400 days at 10% simple interest and at the end of that time you repay your loan plus $500 in interest. How much did you borrow?

29 Interest Principal Rate Time
$500 ? 10% 400 day
P= I / (RT)
500 / (0.1 x 400/365)
4562.5
P = $4,562.50

Question 30

You invest $8,000 on March 3rd and withdraw the money on October 4th. If the interest rate is 9% simple, how much interest did you earn?

30 Interest Principal Rate Time
$8,000 9% Mar 3 to Oct 4
215 days
I = PRT
8000 x 0.09 x 215/365
424.109589
I = $424.11

Question 31

You borrow $7,000 on August 16th and agree to pay back the loan plus interest calculated at 5% simple on June 15th of the next year (not a leap year). How much interest would you pay?

31 Interest Principal Rate Time
$7,000 5% Aug 16 to Jun 15
303 days
I = PRT
7000 x 0.05 x 303/365
290.5479452
I = $290.55

Question 32

You borrow $5,000 on June 15th and agree to pay back the loan plus interest calculated at 8% simple on March 31st of the next year (not a leap year). How much interest would you pay?

32 Interest Principal Rate Time
$5,000 8% Jun 15 to Mar 31
289 days
I = PRT
5000 x 0.08 x 289/365
316.7123288
I = $316.71

Question 33

You put $5,000 into a savings account earning 6% simple interest.

How many months will it take to for you to earn $75 of interest?

How many months will it take for your money to grow to $6,200?

33 a. Interest Principal Rate Time
$75 $5,000 6% ?
T = I / PR
75 / (5000 x 0.06)
0.25
0.35 years
T= 3 months
b. Interest Principal Rate Time
$1,200 $5,000 6% ?
T = I / PR
1200 / (5000 x 0.06)
4
4 years
T= 48 months

Question 34

You invest some money today at 4.5% simple interest for 120 days and the money grows to $7,408. How much did you invest today?

34 Interest Principal Rate Time P + I
? ? 4.5% 120 days $7,408
P + I = P + (PRT)
P (1 + RT)
(P+I) /(1 + RT) = P
P= 7408 /( (1 +0.045 x 120/365) 7408 /( (1 +0.045 x 120/365)
7300
P = $7,300.00
I = 7408 – 7300
I= $ 108.00

Question 35

You invest $12,000 today into a fund that pays 6% simple. How much money will you have in 40 months time?

35 Interest Principal Rate Time
$12,000 6% 40 months
I = PRT
12000 x 0.06 x 40/12
2400
I = $2,400.00
Total Cash $12,000 + $2,400
$14,400

Question 36

You borrow $6,000 to purchase a Jeep and agree to pay back all the money in 3.5 years. How much should you pay back if the interest rate is 12% simple?

36 Interest Principal Rate Time
$6,000 12% 3.5 years
I = PRT
6000 x 0.12 x 3.5
2520
I = $2,520.00
Total Cash $6,000 + $2,520
$8,520

Question 37

You need $6,000 to return to school in 8 months time. How much should you invest today at 6% simple to achieve your goal?

37 Interest Principal Rate Time P + I
? ? 6.0% 8 months $6,000
P + I = P + (PRT)
P (1 + RT)
(P+I) /(1 + RT) = P
P= 6000 /( (1 +0.06 x 8/12) 6000 /( (1 +0.06 x 8/12)
5769.230769
P = $5,769.23

Question 38

A Freedom 35 financial planner claims you will need $1,175,000 to retire in 15 years time. How much should you invest today at 9% simple interest to reach your retirement goal?

38 Interest Principal Rate Time P + I
? ? 9.0% 15 year $1,175,000
P + I = P + (PRT)
P (1 + RT)
(P+I) /(1 + RT) = P
P= 1175000 /( (1 +(0.09 x 15)) 1175000 /( (1 +(0.09 x 15))
500000
P = $500,000.00

Question 39

How long will it take a sum of money to double if it earns 12% simple interest? (Answer in months)

39 Interest Principal Rate Time
$1,000 $1,000 12.0% ?
T = I / PR
1000/ (1000 x 0.12)
8.333333333
T = 100 months

Question 40

You work as a real estate agent for Honest Dave’s Realty Co. located in Burnaby. You have two debts corning due, one in six months for $5,000 and one in 12 months for $6,000. You recently sold a couple of houses and now have some extra cash. How much must you pay today to pay off both debts if interest is 6% simple? Use today as your focal date.

40 Interest Principal Rate Time P + I
? ? 6.0% 6 months $5,000
P = (P+I) /(1 + RT)
5000/( (1+(0.06 x 0.5))
4854.368932
P1 = $4,854.37
Interest Principal Rate Time P + I
? ? 6.0% 12 months $6,000
P = (P+I) /(1 + RT)
6000/( (1+(0.06 x 1))
5660.377358
P2 = $5,660.38
P1 + P2 = $4,854.37 + $5,660.38
$ 10,514.75

Question 41

One of your customers has two debts outstanding, $600 is due 3 months from today and $900 was due 6 months ago. Instead, the customer would like to pay off both debts with a single payment one year from today. Calculate the size of that payment if interest is 12% simple. Use one year from today as the focal date.

41 Interest Principal Rate Time P + I
? $600 12.0% 9 months
P + I = P + (PRT)
600 + (600 x 0.12 x 9/12) 600 + (600 x 0.12 x 9/12)
654
(P + I)1 $654.00
Interest Principal Rate Time P + I
? $900 12.0% 18 months
P + I = P + (PRT)
900 + (900 x 0.12 x 1.5) 900 + (900 x 0.12 x 1.5)
1062
(P + I)1 $1,062.00
P1 + P2 = $654 + $1,062
$ 1,716.00

Question 42

You should have made two car payments of $1,000, 6 months ago and 3 months ago. The bank has agreed to let you repay the loan with equal payments in 3 and 6 months (from today). Calculate the size of these payments if interest is 14% simple. Use 6 months as your focal date.

42 $1,000 $1,000
6 mo ago 3 mo ago today 6 mo
Interest Principal Rate Time P + I
? $1,000 14.0% 12 months
P + I = P + (PRT)
1000 + (1000 x 0.14 x 1) 1000 + (1000 x 0.14 x 1) 1140.00
(P + I)1 $1,140.00
Interest Principal Rate Time P + I
? $1,000 14.0% 9 months
P + I = P + (PRT)
1000 + (1000 x 0.14 x 9/12) 1000 + (1000 x 0.14 x 9/12) 1,105.00
(P + I)2 $1,105.00
Total = 1140 + 1105 2245.00
2245 = (1+0.14*1/4) x + x
1.035 x + x = 2.035 x
2245/ 2.035 = x = $1,103.19

Question 43

You are attempting to repay your line of credit. One year ago you borrowed $5,000 and 6 months ago you borrowed $4,000. You have examined your cash flow projections and decide to repay the line of credit with two payments in 12 and 18 months. The second payment will be $2,000 larger than the first. Find the size of the payments using 18 months as your focal date. Interest is 6% simple.

43 Interest Principal Rate Time P + I
$5,000 6% 30 months
I = PRT
5000 x 0.06 x 30/12 750
Total 5000 + 750 $5,750
Interest Principal Rate Time
$4,000 6% 24 months
I = PRT
4000 x 0.06 x 24/12 480
Total 4000 + 480 $4,480
Value of Payments at Focal Point Value of Payments at Focal Point $10,230
Amount Due = P1 + P2 + 2000 Amount Due = P1 + P2 + 2000
10230 -2000 = 2x
8230 2x
2x = P1(1+ 0.06 x 6/12) + P2 2x = P1(1+ 0.06 x 6/12) + P2
2x = 1.03P1 + P2
8230 = 2.03P
P = 4054.19
P1 = $4,054.19 P1 = $6,054.19

Question 44

You have borrowed from your line of credit. 6 months ago you borrowed $5,000 and today you borrowed $15,000. You plan to pay off the entire line of credit with three equal payments at 3, 5 and 8 months (from today). Find the size of each payment if your bank charges you 9.75% simple interest? Use today as the focal date.

44 Interest Principal Rate Time
$5,000 9.75% 6 months
5000 6 months ago
15000 today I = PRT 5000 x 0.0975 x 0.5 5000 x 0.0975 x 0.5
243.75
Payment 3, 5, 8 months
Focal Date today Interest Principal Rate Time
$15,000 9.75% 6 months
5000 243.75 15000
P0 = $20,243.75
I1 = x/((1+(0.0975* 0.25)) x/((1+(0.0975* 0.25))
I2= x/((1+(0.0975 * 5/12)) x/((1+(0.0975 * 5/12))
I3 = x /((1+(0.0975 * 8/12)) x /((1+(0.0975 * 8/12))
20243.75 = x x x
1.024375 1.040625 1.065
0.976205003 0.960960961 0.938967136
20243.75 = 2.8761331 x
x = 20243.75 $ 7,038.53
2.8761331
Each payment will be Each payment will be $7,038.53

Question 45

Repeat Problem 24 using five months as the focal date. (By comparing the answers to Questions 24 and 25 you will see that it depends slightly on the focal date chosen -but only for simple interest.)

45 Interest Principal Rate Time
$5,000 9.75% 11 months
5000 6 months ago
15000 today I = PRT 5000 x 0.0975 x 11/12 5000 x 0.0975 x 11/12
446.875
Payment 3, 5, 8 months
Focal Date 5 months Interest Principal Rate Time
$15,000 9.75% 5 months
15000*0.0975*5/12 15000*0.0975*5/12
609.375
5000 446.875 15000 609.375
P0 = $21,056.25
-2 months from focal date -2 months from focal date I1 = ((1+(0.0975* 2/12)) ((1+(0.0975* 2/12))
focal date focal date I2=
3 months after focal date 3 months after focal date I3 = ((1+(0.0975 * 3/12)) ((1+(0.0975 * 3/12))
21056.25 = 1.01625 x + x x
1.024375
1.01625 1 0.976205003
21056.25= 2.992455003 x
x = 21056.25 $ 7,036.45
2.992455003
Each payment will be Each payment will be $7,036.45

Question 46

You were supposed to make a payment of $3,500 three months ago and a second payment of $6,100 five months from today. Instead you have arranged with the bank to make a payment one month from now and a second payment, half as large, 6 months from today. Calculate these payments if the bank charges 8.25% simple interest. Use the date of the first unknown payment as the focal date.

46 3500 3 months ago Payment 1, 6 months
6100 5 months forward 5 months forward Focal Date 1 month from now 1 month from now
Interest Principal Rate Time
$3,500 8.25% 4 months
I = PRT 3500 x 0.0825 x 4/12 96.25
Interest Principal Rate Time
$6,100 8.25% 1 months
P = (P+I) /(1 + RT)
6100/ (1 + 0.0825 x 4 /12) 6100/ (1 + 0.0825 x 4 /12) $ 5,936.74
P1 I1 P2 I2
Owing $3,500 96.25 $6,100 -$ 163.26
Owing at Focal Point of one month forward = Owing at Focal Point of one month forward = Owing at Focal Point of one month forward = $9,533
P1 = 2x on Focal point date on Focal point date
P2 = x 5 months forward 5 months forward
I2 (1 +(RT) 1+(0.0825 x 5/12) 1+(0.0825 x 5/12)
$9,533 x x
1.034375
9533 = 2x + 0.966767372 x = 2.966767372 x
x = 9533 3213.261711
2.966767372
2x = 3213.26 x 2 = 6426.52 2x = 3213.26 x 2 = 6426.52
First Payment = $ 6,426.52
Second Payment = $ 3,213.26
$ 9,639.79

Question 47

You borrowed $1,000 on November 30th and another $1,500 on December 31st. Your arrange with the bank to pay the entire amount on February 15th of the following year. If the interest is 12% simple (per annum) how much must you pay on February 15th? Use February 15th as the focal date.

47 Interest Principal Rate Time
$1,000 12% Nov 30 to Feb 15 Nov 30 to Feb 15
77 days
I = PRT 1000 x 0.12 x 77 / 365
$ 25.32
Interest Principal Rate Time
$1,500 12% Dec 31 to Feb 15 Dec 31 to Feb 15
46 days
I = PRT 1500 x 0.12 x 46 / 365
$ 22.68
P1 I1 P2 I2
Payment = $1,000 $ 25.32 $1,500 $ 22.68
$2,548.00

Question 48

You are considering purchasing a car. The owner has offered to let you make two payments of $4,000 each with the first payment at 6 months and the second payment at 10 months. Instead, you would like to make a payment of $4,000 in 8 months and pay the rest today. Find the size of today’s payment if the interest rate is 6% simple. Use today as your focal date.

48 Interest Principal Rate Time P + I
? ? 6.0% 6 months $4,000
P +I = P + PRT P = (P+I)/(1+RT)
P (1 + RT) P (1 + RT) 4000/ (1 + (0.06 x 0.5)
P = (P+I)/(1+RT) (P+I)/(1+RT) $ 3,883.50
Interest Principal Rate Time P + I
? ? 6.0% 10 months $4,000
P = (P+I)/(1+RT)
4000/ (1 + 0.06 x 10/12) 4000/ (1 + 0.06 x 10/12)
$ 3,809.52
Cost of car today = 3883.5 + 3809.52 $ 7,693.02
Interest Principal Rate Time P + I
? ? 6.0% 8 months $4,000
P = (P+I)/(1+RT)
4000/ (1 + (0.06 x 8/12) 4000/ (1 + (0.06 x 8/12)
$ 3,846.15
Payment today = 7693.02 – 3846.15 $ 3,846.87

Question 49

You have two debts coming due. A $1,500 debt is due in 15 months and another debt for $1,000 is due in 33 months. Instead, you would like to repay the debts with two equal payments at 3 and 9 months. Find the size of the equal payments if interest is calculated at 6% simple per year. Use 9 months as your focal date.

49 $1,500 15 months forward 15 months forward Payment 3, 9 months
$1,000 33 months forward 33 months forward Focal Date 9 months from now 9 months from now
Interest Principal Rate Time P + I
? ? 6.0% 6 months $1,500
(15 – 9)
P = (P+I)/(1+RT)
1000/ (1 +(0.06 * 2)) $ 892.86
Interest Principal Rate Time P + I
? ? 6.0% 24 months $1,000
(33 – 9)
P = (P+I)/(1+RT)
1500/(1 + (0.06 x 0.5)) $ 1,456.31
Total due in 9 months = Total due in 9 months = 1456.31 +892.86 $ 2,349.17
$ 2,349.17 = P1 + P2 P1 = x*(1+ 0.06 *0.5) P1 = x*(1+ 0.06 *0.5) 1.03x
P2 = x
$ 2,349.17 =1.03x + x
$ 2,349.17 = 2.03x x = $1,157.23

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