Question

Find the final amount in the following retirement account, in which rate of return on the account and the regular contribution change over time.

$585 per month invested at 6%, compounded monthly, for 5 years; then $776 per month invested at 7%, compounded monthly, for 5 years

Answer 1

To find the final amount in the retirement account, we calculate the future value of the investment in two parts. First, we calculate the future value of the first 5 years with a monthly contribution of $585 at a 6% interest rate compounded monthly. Then, we calculate the future value of the next 5 years with a monthly contribution of $776 at a 7% interest rate compounded monthly. Finally, we add the two future values together to get the total final amount.

Step-by-step explanation:

To find the final amount in the retirement account, we need to calculate the future value of the investment for each period. First, we calculate the future value of the first 5 years with a monthly contribution of $585 at a 6% interest rate compounded monthly. We use the formula:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the monthly contribution, r is the monthly interest rate, and n is the number of periods. Plugging in the values, we get:

1. After 5 years: FV = 585 * ((1 + 0.06/12)^(12*5) - 1) / (0.06/12) ≈ $40,537.57
2. Then, we calculate the future value of the next 5 years with a monthly contribution of $776 at a 7% interest rate compounded monthly:
3. After 5 additional years: FV = 776 * ((1 + 0.07/12)^(12*5) - 1) / (0.07/12) ≈ $70,809.39
4. Finally, we add the two future values together to get the total final amount:
5. Total Final Amount = $40,537.57 + $70,809.39 ≈ $111,346.96