Question

Solve the following problems using either Tables 11-1 or 11-2 from your text. When necessary, create new table factors. (Round new table factors to five decimal places, round dollars to the nearest cent and percents to the nearest hundredth of a percent)

a.Refer to Narrative 11-1. Calculate the compound interest on an investment of $45,000 at 6% interest, compounded quarterly, for 3 years.

b.Refer to Narrative 11-1. You wish to have $17,000 in 11 years. Find how much you should invest now at 12% interest, compounded quarterly in order to have $17,000, 11 years from now. Then calculate the amount of interest.

Table 11-1: Compound Interest Table (Future Value of $1 at Compound Interest) (1 of 2) Periods Periods 1 2 1% 2% 3% 4% 5% 6% 7% 8% 1.00500 1.01000 1.01500 1.02000 1.03000 1.04000 1.05000 1.06000 1.070001.08000 1.01003 1.02010 1.030231.040401.06090 1.081601.10250 1.12360 1.14490 1.16640 1.01508 1.030301.045681.06121 1.092731.124861.15763 1.191021.225041.25971 1,02015 1.04060 106136 1.08243 1.125511.16986 1.21551 1.26248 1.31080 1.36049 1.02525 1.05101 1.07728 1.104081.15927 1.21665 1.27628 1.338231.402551.46933 1.03038 1.06152 1.09344 1.126161.194051.26532 1.34010 1.41852 1.50073 1.50073 1.035531.072141.10984 1.14869 1.22987 1.31593 1.40710 1.50363 1.605781.71382 1.04071 1.08286 1.12649 1.171661.266771.36857 1.47746 1.59385 1.71819 1.85093 1.04591 1.09369 1.14339 1.19509 1.304771.42331 1.551331.689481.83846 1.99900 1.05114 1.10462 1.16054 1.21899 1.34392 1.48024 1.62889 1.79085 1.96715 2.15892 1.05640 1.115671.17795 1.243371.38423 1.53945 1.71034 1.89830 2.10485 2.33164 1.06168 1.12683 1.195621.268241.425761.60103 1.79586 2.01220 2.25219 2.51817 1.06699 1.138091.21355 1.29361 1.46853 1.66507 1.88565 2.13293 2.40985 2.71962 1.07232 1.149471.231761.31948 1.51259 1.731681.979932.260902.57853 2.93719 1.07768 1.16097 1.25023 1.345871.557971.80094 2.078932.39656 2.759033.17217 10 12 13 14 15 CENGAGE Brechner/Bergeman, Contemporary Mathematics for Business & Consumers, 8th Edition 2017 Cengage. All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Table 11-1: Compound Interest Table (Future Value of $1 at Compound Interest) (2 of 2) Periods 1% 1% 2% 3% 4% 5% 6% 7% 8% Periods 16 1.08307 1.17258 1.26899 1.37279 1.60471 1.87298 2.18287 2.54035 2.95216 3.42594 16 1,08849 1.18430 1.28802 1.400241.65285 1.94790 2.29202 2.69277 3.15882 3.70002 17 1,09393 1.19615 1.30734 1.42825 1.70243 2.02582 2.40662 2.85434 3.37993 3.99602 1.09940 1.20811 1.32695 1.45681 1.75351 2.10685 2.52695 3.02560 3.61653 4.31570 1.10490 1.22019 1.34686 1.485951.80611 2.19112 2.65330 3.20714 3.86968 | 4.66096 1.11042 1.23239 1.36706 1.51567 1.86029 2.27877 2.78596 3.39956 4.14056 5.03383 1.11597 1.24472 1.38756 1.54598 1.91610 2.36992 2.92526 3.60354 4.43040 5.43654 1.12155 1.25716 1.40838 1.576901.97359 2.46472 3.07152 3.81975 4.740535.87146 23 1.12716 1.26973 1.42950 1.60844 2.03279 2.56330 3.22510 4.04893 5.07237 6.34118 24 25 1.13280 1.28243 1.45095 1.64061 2.09378 2.66584 3.38635 4.29187 5.42743 6.84848 25 12 ENGAGE Brechner/Bergeman, Contemporary Mathematics for Business & Consumers, 8th Edition 2017 Cengage. All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part EXHIBIT 11-3: Compounding Periods per Year

Answer 1

a) In the question, it is not given that 6% is for per annum therefore I am assuming it to be for a quarter only.

Now the formula for Compound Interest(C.I.) - Present Value* [(100+ Interest%)/100]Power=The no. of times interest is compounded- Present Value

or

C.I.= Present Value*Future value Annuity Factor-Present Value

So, C.I.    = 45000*Future value annuity factor of 12 quarters at 6% rate of interest

= 45000*2.01220-45000

Answer = $90549-45000= $45,549

b) Now, the formula for Present value = Future value* 1/Compounded value annuity factor of 44 quarters at 12% rate of interest

= 17000*1/146.41750

= $116.10