Mrs. Carter deposits $100 in the bank at the end of each month. If the bank pays (a) 6% per year, (b) 7% per year, compounded monthly, how much money will she have accumulated at the end of 5 years? 36 DISCRETE, PERIODIC COMPOUNDING [CHAP. 4 (a) The effective monthly interest rate is 6%/12=0.5%. There will be a total of 5x12= 60 monthly payments. Hence, using Appendix A, F=$100(F/A, 0.5%, 60) = $100(69.7700) = $6977.00 (b) The effective monthly interest rate is 7%/12=0.583333 %. As the tabulated value of (F/A, 0.583333%, 60) is not readily available, we interpolate linearly between (F/A, 0.5%, 60) and (F/A, 0.75%, 60). (F/A, 0.583333%, 60)69.7700+ 0.583333-0.5 0.75 -0.5 (75.4241-69.7700)=71.6547 and F=$100(71.6547)= $7165.47 Another (and more accurate) way to solve this problem is to apply (2.3): F=$100 (1+0.00583333)-1 $100- 0.417625 = $7159.29 0.00583333 0.00583333 4.12 In Problem 4.11, suppose that Mrs. Carter deposits $100 a month during the first year, $110 a month during the second year, $120 a month during the third year, etc. How much will have accumulated at the end of 5 years if the interest rate is 6% per year, compounded monthly? Treating each year separately, F = $100(F/A, 0.5%, 12) (F/P,0.5%, 48)+ $110(F/A, 0.5%, 12) (F/P,0.5%, 36) +$120(F/A, 0.5%, 12) (F/P, 0.5%, 24) +$130(F/A, 0.5%, 12) (F/P,0.5%, 12) +$140(F/A, 0.5%, 12)
