As a fringe benefit for the past 8 years, Colin's employer has contributed $50 at the end of each month into an employee retirement account for Colin that pays interest at the rate of 8%/year compounded monthly. Colin has also contributed $2,000 at the end of each of the last 4 years into an IRA that pays interest at the rate of 10%/year compounded yearly. How much does Colin have in his retirement fund at this time?
A) $9,282.00
B) $9,813.83
C) $6,693.43
D) $15,975.43

Question

As a fringe benefit for the past 8 years, Colin's employer has contributed $50 at the end of each month into an employee retirement account for Colin that pays interest at the rate of 8%/year compounded monthly. Colin has also contributed $2,000 at the end of each of the last 4 years into an IRA that pays interest at the rate of 10%/year compounded yearly. How much does Colin have in his retirement fund at this time? ​
A) $9,282.00
B) $9,813.83
C) $6,693.43
D) $15,975.43

Quizplus · Accepted Answer

The total amount in Colin's retirement fund can be calculated by adding the future value of the employer's contributions and the future value of Colin's contributions to his IRA. For the employer's contributions, we use the formula for the future value of an annuity: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the monthly interest rate, and $n$ is the total number of payments. Given that the employer contributes $50 at the end of each month for 8 years at an annual interest rate of 8% compounded monthly, we have $P = 50$, $r = \frac{0.08}{12}$, and $n = 8 \times 12$. For Colin's IRA contributions, since he contributes $2,000 at the end of each of the last 4 years at an annual interest rate of 10% compounded yearly, we can calculate the future value of each contribution at the present time and sum them up. The formula for the future value of a single sum is $FV = P \times (1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years until maturity. Calculating both parts and adding them together gives the total amount in Colin's retirement fund, which matches the value provided in option D, $15,975.43. This accounts for both the compounded growth of the employer's monthly contributions and the compounded annual growth of Colin's yearly IRA contributions.

As a Fringe Benefit for the Past 8 Years, Colin's