{"id":565,"date":"2020-04-30T20:04:53","date_gmt":"2020-05-01T00:04:53","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=565"},"modified":"2024-10-29T15:11:10","modified_gmt":"2024-10-29T19:11:10","slug":"review-questions-for-chapter-4","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/review-questions-for-chapter-4\/","title":{"raw":"Review Questions for Chapter 4","rendered":"Review Questions for Chapter 4"},"content":{"raw":"Click on the question number to get to the solution.<\/em>\r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Time<\/strong><\/td>\r\nInterest<\/strong><\/td>\r\nBalances:<\/strong><\/td>\r\n<\/tr>\r\n<\/thead>\r\n
0m<\/td>\r\n<\/td>\r\n$8,000.00<\/td>\r\n<\/tr>\r\n
3m<\/td>\r\n$200.00<\/td>\r\n$8,200.00<\/td>\r\n<\/tr>\r\n
6m<\/td>\r\n$205.00<\/td>\r\n$8,405.00<\/td>\r\n<\/tr>\r\n
9m<\/td>\r\n$210.13<\/td>\r\n$8,615.13<\/td>\r\n<\/tr>\r\n
12m<\/td>\r\n$215.37<\/td>\r\n$8,830.50<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote] Complete the following table, assuming an interest rate of 10% compounded quarterly.\r\n\r\n \r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Time<\/strong><\/td>\r\nInterest<\/strong><\/td>\r\nBalance<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/thead>\r\n
0<\/td>\r\n0<\/td>\r\n$8,000.00<\/td>\r\n(PV)<\/td>\r\n<\/tr>\r\n
3 months\r\n\r\n6 months<\/td>\r\n$200.00<\/td>\r\n \r\n\r\n8,405.00<\/td>\r\n<\/td>\r\n<\/tr>\r\n
9 months<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
12 months<\/td>\r\n<\/td>\r\n8,830.50<\/td>\r\n(FV)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Time<\/td>\r\nInterest<\/td>\r\nBalances:<\/td>\r\n<\/tr>\r\n
0m<\/td>\r\n<\/td>\r\n$12,000.00<\/td>\r\n<\/tr>\r\n
lm<\/td>\r\n$150.00<\/td>\r\n$12,150.00<\/td>\r\n<\/tr>\r\n
2m<\/td>\r\n$151.88<\/td>\r\n$12,301.88<\/td>\r\n<\/tr>\r\n
3m<\/td>\r\n$153.77<\/td>\r\n$12,455.65<\/td>\r\n<\/tr>\r\n
4m<\/td>\r\n$155.70<\/td>\r\n$12,611.35<\/td>\r\n<\/tr>\r\n
5m<\/td>\r\n$157.64<\/td>\r\n$12,768.99<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote] Make a table with the same headings as previous, but for a loan of $12,000 for 5 months at 15% compounded monthly.\r\n\r\n \r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Nominal Rate<\/td>\r\nFrequency<\/td>\r\nNominal Rate, jm<\/td>\r\nPeriodic rate, i<\/td>\r\n<\/tr>\r\n
8%<\/td>\r\nsemi-annually<\/td>\r\nj2<\/sub> = 0.08<\/td>\r\ni =0.04<\/td>\r\n<\/tr>\r\n
15%<\/td>\r\nmonthly<\/td>\r\nj12<\/sub> = 0.15<\/td>\r\ni = 0.0125<\/td>\r\n<\/tr>\r\n
10%<\/td>\r\nquarterly<\/td>\r\nj4<\/sub> = 0.10<\/td>\r\ni= 0.025<\/td>\r\n<\/tr>\r\n
9%<\/td>\r\nannually<\/td>\r\nj1<\/sub> = 0.09<\/td>\r\ni= 0.09<\/td>\r\n<\/tr>\r\n
10.4%<\/td>\r\nweekly<\/td>\r\nj52<\/sub> = 0.104<\/td>\r\ni= 0.002<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote] Write the following nominal rates in the \"jm<\/sub><\/em>\" notation and find the corresponding periodic rates, i (include the period with these). The first line is completed as an example.\r\n\r\n \r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Nominal Rate<\/strong><\/td>\r\nFrequency<\/strong><\/td>\r\nNominal Rate, jm<\/sub><\/em><\/strong><\/td>\r\nPeriodic rate, i<\/em><\/strong><\/td>\r\n<\/tr>\r\n
8%<\/td>\r\nsemi-annually<\/td>\r\nj2<\/sub><\/em>= 0.08<\/td>\r\ni<\/em> =0.04<\/td>\r\n<\/tr>\r\n
15%<\/td>\r\nmonthly<\/td>\r\n?<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
10%<\/td>\r\nquarterly<\/td>\r\n?<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
9%<\/td>\r\nannually<\/td>\r\n?<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
10.4%<\/td>\r\nweekly<\/td>\r\n?<\/td>\r\n?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Nominal Rate<\/strong><\/td>\r\nCompounding Frequency<\/strong><\/td>\r\nNominal Rate, jm<\/sub><\/em><\/strong><\/td>\r\nPeriodic Rate, i<\/em><\/strong><\/td>\r\n<\/tr>\r\n
7%<\/td>\r\nannually<\/td>\r\njl<\/sub><\/em> = 7%<\/td>\r\ni<\/em>= 0.07<\/td>\r\n<\/tr>\r\n
9%<\/td>\r\nquarterly<\/td>\r\nj4<\/sub> <\/em>= 9%<\/td>\r\ni<\/em> = 0.0225<\/td>\r\n<\/tr>\r\n
6%<\/td>\r\nmonthly<\/td>\r\nj12<\/sub><\/em> = 6%<\/td>\r\ni<\/em> = 0.005<\/td>\r\n<\/tr>\r\n
12%<\/td>\r\nquarterly<\/td>\r\nj4<\/sub><\/em> = 12%<\/td>\r\ni<\/em> = 0.03<\/td>\r\n<\/tr>\r\n
24%<\/td>\r\nmonthly<\/td>\r\nj12<\/sub><\/em> = 24%<\/td>\r\ni<\/em> = 0.02<\/td>\r\n<\/tr>\r\n
17%<\/td>\r\nsemi-annually<\/td>\r\nj2<\/sub> <\/em>= 17%<\/td>\r\ni<\/em> = 0.085<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote] Write each of the following rates as nominal rates and complete the table.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Nominal Rate<\/strong><\/td>\r\nCompounding Frequency<\/strong><\/td>\r\nNominal Rate, jm<\/sub><\/em><\/strong><\/td>\r\nPeriodic Rate, i<\/em><\/strong><\/td>\r\n<\/tr>\r\n
?<\/td>\r\n?<\/td>\r\njl<\/sub> <\/em>= 7%<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
?<\/td>\r\n?<\/td>\r\nj4<\/sub><\/em> = 9%<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
?<\/td>\r\n?<\/td>\r\nj12<\/sub><\/em> = 6%<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
?<\/td>\r\nQuarterly<\/td>\r\n?<\/td>\r\n<\/td>\r\n<\/tr>\r\n
?<\/td>\r\nMonthly<\/td>\r\n?<\/td>\r\n<\/td>\r\n<\/tr>\r\n
?<\/td>\r\nSemi-annually<\/td>\r\n?<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n
PV<\/td>\r\nInterest Rate<\/td>\r\nLength<\/td>\r\ni<\/em><\/td>\r\nn<\/em><\/td>\r\nFV<\/td>\r\n<\/tr>\r\n
$11,500<\/td>\r\n9% quarterly<\/td>\r\n2 years<\/td>\r\n0.0225<\/td>\r\n8<\/td>\r\n$13,740.56<\/td>\r\n<\/tr>\r\n
$7,400<\/td>\r\n6% annually<\/td>\r\n4 years<\/td>\r\n0.06<\/td>\r\n4<\/td>\r\n$9,342.33<\/td>\r\n<\/tr>\r\n
$14,000<\/td>\r\n8.6% monthly<\/td>\r\n8 months<\/td>\r\n0.007166<\/td>\r\n8<\/td>\r\n$14,823.09<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote] Complete the following table, using the compound-interest formula to calculate the future value of each loan.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
PV<\/td>\r\nInterest Rate<\/td>\r\nLength<\/td>\r\ni<\/em><\/td>\r\nn<\/em><\/td>\r\nFV<\/td>\r\n<\/tr>\r\n
$11,500<\/td>\r\n9% compounded quarterly<\/td>\r\n2 years<\/td>\r\n?<\/td>\r\n?<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
$7,400<\/td>\r\n6% compounded annually<\/td>\r\n4 years<\/td>\r\n?<\/td>\r\n?<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
$14,000<\/td>\r\n8.6% compounded monthly<\/td>\r\n8 months<\/td>\r\n?<\/td>\r\n?<\/td>\r\n?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Year<\/td>\r\nInterest<\/td>\r\nBalances<\/td>\r\n<\/tr>\r\n
0<\/td>\r\n<\/td>\r\n$1,000.00<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n$85.00<\/td>\r\n$1,085.00<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n$92.23<\/td>\r\n$1,177.23<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n$100.06<\/td>\r\n$1,277.29<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote] Government compound-interest savings bonds have the interest compounded every year. Suppose that a $1,000 bond paid interest at 8.5% compounded annually and was kept for three years. Find the value (Future Value) of the bond at the end of the three years by:\r\n
    \r\n \t
  1. Showing the interest and balance each year.<\/li>\r\n \t
  2. Using the compound-interest formula to get FV at the end of two years.<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote] $31,459.10\r\n\r\n[\/footnote] A loan of $24,000 for two years is to carry interest at 14% compounded semi-annually. Use the compound-interest formula to find the value of the loan at the end of two years.\r\n\r\n \r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    a. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Year<\/td>\r\nBalance<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n$1,000.00<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n$1,250.00<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n$1,562.50<\/td>\r\n<\/tr>\r\n
    3<\/td>\r\n$1,953.13<\/td>\r\n<\/tr>\r\n
    4<\/td>\r\n$2,441.41<\/td>\r\n<\/tr>\r\n
    5<\/td>\r\n$3,051.76<\/td>\r\n<\/tr>\r\n
    6<\/td>\r\n$3,814.70<\/td>\r\n<\/tr>\r\n
    7<\/td>\r\n$4,768.38<\/td>\r\n<\/tr>\r\n
    b.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Year<\/td>\r\nBalance<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n$1,000.00<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n$1,250.00<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n$1,500.00<\/td>\r\n<\/tr>\r\n
    3<\/td>\r\n$1,750.00<\/td>\r\n<\/tr>\r\n
    4<\/td>\r\n$2,000.00<\/td>\r\n<\/tr>\r\n
    5<\/td>\r\n$2,250.00<\/td>\r\n<\/tr>\r\n
    6<\/td>\r\n$2,500.00<\/td>\r\n<\/tr>\r\n
    7<\/td>\r\n$2,750.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote] A \"junk\" bond was supposed to pay interest at 25% paid annually. Unfortunately, no payments were made for the last seven years, so the interest was allowed to compound at 25% compounded annually.\r\n
      \r\n \t
    1. Find the value at the end of each of the seven years for a bond with a principal of $1,000 at the start.<\/li>\r\n \t
    2. Also find the value the loan would have had at the end of each year if the interest had been simple interest at 25% annually. Note the difference caused by compounding.<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n
      PV<\/td>\r\nInterest Rate<\/td>\r\nLength<\/td>\r\nn<\/td>\r\nFV<\/td>\r\n<\/tr>\r\n
      $11,500<\/td>\r\n6.5% compounded semi-annually<\/td>\r\n2 years<\/td>\r\n8<\/td>\r\n$11,364.76<\/td>\r\n<\/tr>\r\n
      $7,400<\/td>\r\n16% compounded monthly<\/td>\r\n3.5 years<\/td>\r\n4<\/td>\r\n$25,000.00<\/td>\r\n<\/tr>\r\n
      $14,000<\/td>\r\nI0% compounded quarterly<\/td>\r\n1 year<\/td>\r\n8<\/td>\r\n$30,000.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote] Find the present values of each of the amounts below, filling in the rest of the table when you do so.\r\n\r\n\r\n\r\n\r\n\r\n\r\n
      PV<\/td>\r\nInterest Rate<\/td>\r\nLength<\/td>\r\nn<\/em><\/td>\r\nFV<\/td>\r\n<\/tr>\r\n
      ?<\/td>\r\n6.5% compounded semi-annually<\/td>\r\n2 years<\/td>\r\n?<\/td>\r\n$11,364.76<\/td>\r\n<\/tr>\r\n
      ?<\/td>\r\n16% compounded monthly<\/td>\r\n3.5 years<\/td>\r\n?<\/td>\r\n$25,000.00<\/td>\r\n<\/tr>\r\n
      ?<\/td>\r\nI0% compounded quarterly<\/td>\r\n1 year<\/td>\r\n?<\/td>\r\n$30,000.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nCheck your last result by assuming the PV was invested for one year in an account paying 10% compounded quarterly and adding on the interest each period as in Problem 1.\r\n\r\n \r\n\r\n[footnote]\r\n
        \r\n \t
      1. $38,980.40<\/li>\r\n \t
      2. $39,959.34<\/li>\r\n \t
      3. $40,963.72<\/li>\r\n<\/ol>\r\n[\/footnote] According to the terms of his uncle's will, Tom Jones is to receive $50,000 2.5 years from now. Tom would like to borrow as much as he can now and pay it off with his inheritance. Use the compound-interest formula to find out how much he can borrow if the interest rate is as follows:\r\n
          \r\n \t
        1. 10% compounded monthly.<\/li>\r\n \t
        2. 9% compounded monthly.<\/li>\r\n \t
        3. 8% compounded monthly.<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote]$5,591.10\r\n\r\n[\/footnote] Ann Lee has a lease on a government property which must be paid by a lump sum of $6,000 every year. The next payment is due in 10 months from now, and Ann plans to invest enough money in an account at her bank so that the amount in the account in 10 months will cover the $6,000 payment. If the interest rate is 8.5% compounded monthly, how much should she place in the account?\r\n\r\n \r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n
          Year<\/td>\r\nBalance<\/td>\r\n<\/tr>\r\n
          1<\/td>\r\n$81,000.00<\/td>\r\n<\/tr>\r\n
          2<\/td>\r\n$54,910.00<\/td>\r\n<\/tr>\r\n
          3<\/td>\r\n$60,950.10<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nb.\r\n\r\n$100,000 (1.11)3<\/sup> = $30,000 (1.11)2<\/sup> + $35,000 (1.11) + x<\/em>\r\n\r\nx\u00a0 = $60,950.10\r\n\r\n[\/footnote] Ajax Company is borrowing $100,000 now and has agreed to pay 11% compounded annually on the outstanding balance at all times. Ajax plans to pay $30,000 at the end of the first year of the loan and $35,000 at the end of the second year. The remaining debt is to be completely paid off by a single payment at the end of the third year. Draw a cash-flow diagram and find the amount that should be paid at the end of the third year by:\r\n
            \r\n \t
          1. Finding the interest and balance due at the end of each year.<\/li>\r\n \t
          2. Using an equation of value at a focal date (e.g., at year 3).<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote]\r\n\r\na. $37,684.65\u00a0\u00a0\u00a0\u00a0 b. $38,876.54\r\n\r\n[\/footnote] AC Holdings has taken over a company with a debt that was to be paid by a payment of $85,000 one year from now. Instead, AC has agreed with the holder of the debt to pay it off early and be allowed 12% compounded quarterly for early payment. It plans to pay $40,000 now and the rest in six months.\r\n
              \r\n \t
            1. Draw a cash-flow diagram and find the amount that should be paid in 6 months.<\/li>\r\n \t
            2. Repeat (a) but assume the payments now and in 6 months are to be equal in size.<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote]\r\n
                \r\n \t
              1. $23,685.88<\/li>\r\n \t
              2. FV = $ 23,685(1.07)1.5<\/sup> =$ 20,000(1.07)4<\/sup> =$ 26,215.92<\/li>\r\n<\/ol>\r\n[\/footnote] North Credit Union advertises that it will pay 7% compounded annually on money on deposit for periods longer than one year and that the money may be taken out, with interest, at any time after the first year. A depositor placed $20,000 on deposit at the above rate for four years, but decided to withdraw it after 2.5 years.\r\n
                  \r\n \t
                1. How much should the depositor receive?<\/li>\r\n \t
                2. Show that, if this amount were deposited at the same rate for the remaining 1.5 years, the result would be the same as if it had never been withdrawn.<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote]\r\n
                    \r\n \t
                  1. \u00a08% compounded quarterly<\/li>\r\n \t
                  2. 8.08% compounded semi-annually<\/li>\r\n<\/ol>\r\n[\/footnote] A loan of $17,000 for three years resulted in a future value of $21,560.11. Use your calculator functions to find the nominal interest rate if the loan was compounded:\r\n
                      \r\n \t
                    1. \r\n
                        \r\n \t
                      1. quarterly<\/li>\r\n \t
                      2. semi-annually.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote]\r\n\r\n16% compounded quarterly = 15.7913% compounded monthly\r\n\r\n[\/footnote] Use your calculator functions to find the FV of a principal of $1.00 invested for one year at 16% compounded quarterly, and leave the results in your calculator. Then find the nominal monthly rate that will give the same FV - the rate compounded monthly that is equivalent to 16% compounded quarterly. Check your answer by finding the future value of a principal of $10,000 invested for two years at each rate. You should get the same answer in each case.\r\n\r\n \r\n\r\n[footnote]\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                        Effective Rate, j1<\/sub><\/em><\/strong><\/td>\r\nj2<\/sub><\/strong><\/em><\/td>\r\nj4<\/sub><\/strong><\/em><\/td>\r\nj12<\/sub><\/strong><\/em><\/td>\r\n<\/tr>\r\n
                        17.227080%<\/td>\r\n16.214281%<\/td>\r\n16.542910%<\/td>\r\n16%<\/td>\r\n<\/tr>\r\n
                        12.550881%<\/td>\r\n12.180000%<\/td>\r\n12%<\/td>\r\n11.881961%<\/td>\r\n<\/tr>\r\n
                        9.202500%<\/td>\r\n9%<\/td>\r\n8.900966%<\/td>\r\n8.835748%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/footnote]\u00a0\u00a0\u00a0\u00a0 Complete\u00a0 the following table of equivalent nominal rates, giving answers in percent to six decimals.\u00a0 Each row will contain equivalent rates.\r\n<\/span>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                        Effective Rate, j1<\/sub><\/em><\/td>\r\nj2<\/sub><\/em><\/td>\r\nj4<\/sub><\/em><\/td>\r\nj12<\/sub><\/em><\/td>\r\n<\/tr>\r\n
                        ?<\/td>\r\n?<\/td>\r\n?<\/td>\r\nj12 <\/sub><\/em>= 16%<\/td>\r\n<\/tr>\r\n
                        ?<\/td>\r\n?<\/td>\r\nj4 <\/sub><\/em>= 12%<\/td>\r\n?<\/td>\r\n<\/tr>\r\n
                        ?<\/td>\r\nj2<\/sub><\/em> = 9%<\/td>\r\n?<\/td>\r\n?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n[footnote]\r\n
                          \r\n \t
                        1. $5,076.94<\/li>\r\n \t
                        2. $5,076.94<\/li>\r\n \t
                        3. $5,076.94<\/li>\r\n \t
                        4. $5,076.94 (using a fractional period )<\/li>\r\n<\/ol>\r\n[\/footnote]\u00a0 Use your results in Row 1 in the previous problem to find the future value of a loan of $4,000 for 18 months by doing the compounding:\r\n
                            \r\n \t
                          1. monthly.<\/li>\r\n \t
                          2. Quarterly.<\/li>\r\n \t
                          3. Semi-annually<\/li>\r\n \t
                          4. Annually<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote] $4,416.96\r\n\r\n[\/footnote]\u00a0 Your first child was born this year and you decide to save for her education. You deposit $2,000 into an RESP (registered education savings plan) that pays 4.5% compounded annually (j1<\/sub><\/em>=0.045). How much will your child have in 18 years? Use both the formula and the TVM Keys.\r\n\r\n \r\n\r\n[footnote] $6,400.42\r\n\r\n[\/footnote] You borrow $5,000 from a private loan company and agree to pay it back with interest calculated at 10% compounded quarterly. How much will you owe in 30 months? Use both the formula and the TVM Keys.\r\n\r\n \r\n\r\n[footnote] $2,868.47\r\n\r\n[\/footnote] You are expecting a tax refund of $3,000 six months from now. You take your T4 slips to H&P Square Tax preparation service and they agree to give you the money now if you sign over the refund to them. How much money will you receive today if interest is calculated at j12<\/sub><\/em> = 9$%. Use both the formula and the TVM Keys.\r\n\r\n \r\n\r\n[footnote]$11,506.98\r\n\r\n[\/footnote] You go to purchase a brand new motorcycle and the dealer quotes you a price of $14,000 to be paid as a single payment in 30 months. You would like to pay cash today for the motorcycle. How much should you offer if interest is calculated at 8% compounded semi\u00ad annually? Use the formula and the TVM Keys.\r\n\r\n \r\n\r\n[footnote] $590,856.82\r\n\r\n[\/footnote] You have $75,000 and decide to purchase a 30 year Government of Canada strip bond with an interest rate of 7.0% compounded semi-annually. How much will the bond be worth in 30 years? (i.e., what is the maturity value of the strip bond?)\r\n\r\n \r\n\r\n[footnote]\r\n
                              \r\n \t
                            1. \u00a0$126,934.31<\/li>\r\n \t
                            2. \u00a08.82331%<\/li>\r\n \t
                            3. \u00a037.65 years<\/li>\r\n<\/ol>\r\n[\/footnote] Financial planners predict you will need one million dollars to retire.\r\n
                                \r\n \t
                              1. You would like to buy a 30-year strip bond with an interest rate of 7% compounded semi-annually that has a maturity value of one million dollars. How much will you need to pay for this strip bond today?<\/li>\r\n \t
                              2. Unfortunately, you only have $75,000 available to buy a bond. You are considering buying a junk bond (risky bond) because you know that the interest rates are much. higher than for a Government of Canada bond. What nominal interest rate, compounded semi-annually, do you require so that the bond will have a maturity value of $1,000,000 in 30 years?<\/li>\r\n \t
                              3. Your friend convinces you that junk bonds are too risky to be used as a retirement investment. If instead, you buy the Government of Canada bond (with your $75,000) that pays 7% compounded semi-annually, how many years will it take you to reach your goal of having $1,000,000?<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote]\r\n\r\nj4<\/sub><\/em> = 21.44411%\r\n\r\n[\/footnote]\u00a0 If an investment grows from $10,000 to $16,000 in 27 months, what was the nominal rate of interest, compounded quarterly?\r\n\r\n \r\n\r\n[footnote]\r\n
                                  \r\n \t
                                1. \u00a0j12<\/sub><\/em> = 10.17956%<\/li>\r\n \t
                                2. \u00a0j4<\/sub><\/em>\u00a0 = 10.26616%<\/li>\r\n \t
                                3. \u00a0j2<\/sub><\/em> = 10.39790%<\/li>\r\n \t
                                4. \u00a0j1<\/sub><\/em> = 10.66819%<\/li>\r\n<\/ol>\r\n[\/footnote] \u00a0\u00a0\u00a0 If an investment grows from $4,000 to $6,000 in 48 months, what was the nominal rate of interest:\r\n
                                    \r\n \t
                                  1. compounded monthly?<\/li>\r\n \t
                                  2. compounded quarterly?<\/li>\r\n \t
                                  3. compounded semi-annually?<\/li>\r\n \t
                                  4. compounded annually?<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote] 5.5 years\r\n\r\n[\/footnote] You would like to save to return to school. You deposit $4,000 into a GIC that pays . You have decided to return to school when your savings grows to at least $6,000. If you make no more contributions, how many years will it take you to reach your goal?\r\n\r\n \r\n\r\n[footnote] 5.0 years\r\n\r\n[\/footnote] How many years will it take $300.00 to accumulate to $425.29 at 7% compounded monthly?\r\n\r\n \r\n\r\n[footnote] 7.0000%\r\n\r\n[\/footnote] An investment of $1,500.00 made 27 months ago is now worth $1753.48. What nominal rate of interest, compounded quarterly, did this investment earn?\r\n\r\n \r\n\r\n[footnote] 1.5 years\r\n\r\n[\/footnote] You have always wanted to go to Orlando, Florida. You estimate you will need $6,000 for your trip. You deposit your tax refund of $5,016.10 into an account that pays 12% compounded monthly. How many years will it take to reach $6,000?\r\n\r\n \r\n\r\n[footnote] $7,457.11 (the interest earned is $2,457.11)\r\n\r\n[\/footnote] You put $5,000 into a 3-year term deposit that pays interest at 6.3% compounded quarterly. After the end of the three years you renew the term deposit plus accumulated interest at 7.2% compounded semi\u00ad annually for an additional three years.\r\n
                                      \r\n \t
                                    1. How much money will you have at the end of the six years?<\/li>\r\n \t
                                    2. How much interest did you earn?<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote] $10,000 (the interest paid is $15,292.49)\r\n\r\n[\/footnote] You borrowed some money from the Honest Shark Finance Co. You made only one payment of $25,292.49 at the end of 5 years to pay off the loan. The interest rate was 18.5% compounded semi\u00ad annually for the first 2 years and 19.6% compounded quarterly for the remaining years.\r\n
                                        \r\n \t
                                      1. How much did you borrow?<\/li>\r\n \t
                                      2. How much interest did you pay?<\/li>\r\n<\/ol>\r\n \r\n\r\n[footnote] In today's dollars the 2nd option is worth $17,708.60\u00a0 which is less than $18,000 so the second option is cheaper\r\n\r\n[\/footnote] You are going to purchase a car and are given two options to pay.\r\n