Assume that you contribute $100 per month to a retirement plan for 20 years. Then you are able to increase the contribution to $200 per month for another 20 years. Given a 6 percent interest rate, what is the value of your retirement plan after 40 years?
A) $225,353
B) $19,155
C) $245,353
D) $199,359

Question

Quizplus · Accepted Answer

To calculate the future value of a series of cash flows (contributions) at a given interest rate, we use the future value of an annuity formula. For the first 20 years, with monthly contributions of $100 and an annual interest rate of 6% (or 0.5% monthly), the future value can be calculated using the formula for the future value of an annuity. Then, for the next 20 years, with monthly contributions of $200 at the same interest rate, we calculate the future value of these contributions and add it to the future value of the first set of contributions compounded for another 20 years.First 20 years: $FV_1 = P \times \frac{(1 + r)^n - 1}{r}$- $P = \$100$, $r = 0.06/12$, $n = 20 \times 12$Next 20 years: $FV_2 = P \times \frac{(1 + r)^n - 1}{r}$- $P = \$200$, $r = 0.06/12$, $n = 20 \times 12$The future value of the first 20 years' contributions also needs to be compounded for the next 20 years:- $FV_{1,compounded} = FV_1 \times (1 + r)^n$The total future value ($FV_{total}$) is the sum of $FV_{1,compounded}$ and $FV_2$.Given the complexity of the calculation and the need for precision, using a financial calculator or spreadsheet is recommended to accurately compute these values. The correct answer, based on these calculations, is approximately $245,353, which accounts for both the contributions and the compound interest over the 40-year period.

Assume That You Contribute $100 Per Month to a Retirement