Chapter 3 Review Questions

Do not forget to draw your time diagrams!

^[1] For each principal, rate and time given below, compute the interest:

1. $2,500 at 14.2% for 1.5 years.
2. $3,200 at 8.75% for 16 months.
3. $8,300 at 11.2% for 160 days.
4. $800 at 13.6% for 212 days.

^[2] Calculate the interest for each of the following loans:

1. $850 at 11.5% from June 14, 2022 to October 19, 2022.
2. $2,800 at 11.25% from September 9, 20199 to March 19, 2020. (2020 was a leap year!)
3. $4,100 at 7.5% from July 15, 2022 to September 6, 2022.

^[3] Complete each row in the following table:

^[4] Find the interest rate which will pay $36.40 interest on a principal of $2,140 borrowed for 69 days.

^[5] If a loan of $1,900 borrowed from October 22, 2021 to December 17, 2021 resulted in $33.85 interest, what was the simple interest rate charged?

^[6] What principal will earn $95.20 if borrowed at 13.5% for 4 months?

^[7] How many days will it take for a principal of $19,200 to earn $650.00 interest at 10%?

^[8] What is the future value of $1,680 over 260 days at 11.25%?

^[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.

^[10] If 9 months interest at 8.725% is $186.20, what principal was borrowed?

^[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?

^[12] If the future value of a loan for 222 days at 11.75% was $937.72, what was the principal of the loan?

^[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?

^[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.)

^[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 .

^[16] AW borrowed $9,000 on January 30, 2022 and agreed to pay 14% simple interest on the balance outstanding at any time. She paid $5,000 on March 9, 2022 and $2,500 on May 25, 2022. How much will she have to pay on June 30, 2022 in order to pay off the debt? Use June 30, 2022 as the focal date.

^[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.

^[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.

^[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.

^[20] Find the present values of the following payments if money is worth 8%:

1. $2,800 to be paid in 60 days.
2. $950 to be paid in 120 days.
3. $56,000 to be paid in 1 year.

^[21] You invest $1,000 for 4 years at 8% simple interest. How much interest will you earn?

^[22] You invest $6,000 for 2.5 years at 9% simple interest. How much interest will you earn?

^[23] $6,000 earns $180 in interest when invested for 30 months. What simple rate of interest is being paid?

^[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?

^[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?

^[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?

^[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?

^[28] You invest $1,000 for 18 months at 8% simple interest. How much interest will you earn?

^[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?

^[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?

^[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?

^[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?

^[33] You put $5,000 into a savings account earning 6% simple interest.

1. How many months will it take to for you to earn $75 of interest?
2. How many months will it take for your money to grow to $6,200?

^[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?

^[35]  You invest $12,000 today into a fund that pays 6% simple. How much money will you have in 40 months time?

^[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?

^[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?

^[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?

^[39] How long will it take a sum of money to double if it earns 12% simple interest? (Answer in months)

^[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.

^[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.

^[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.

^[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.

^[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.

^[45]  Repeat the previous problem using five months as the focal date. (By comparing the answers to both questions you will see that it depends slightly on the focal date chosen -but only for simple interest.)

^[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.

^[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.

^[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.

^[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.