Question 4.P.12: In Problem 4.11, suppose that Mrs. Carter deposits $100 a mo......
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?
Step-by-Step
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)
The required numerical values can be obtained from Appendix A (using interpolation in some cases), or from (2.1) and (2.3).
F/P = (1 + i)” (2.1)
F/A = \frac{(1 + i)^n – 1}{i} (2.3)F = [$100(1.2705) + $110(1.1967) + $120(1.1272) + $130(1.0617) + $140](12.3356)
= ($671.972)(12.3356) = $8289.18
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