Question 50

$5,653.34

To achieve a balance of $15,000 in 20 years at an annual interest rate of 5 percent, compounded annually, an investment of $5,653.34 is required today. This amount reflects the present value calculation necessary to reach the desired future sum.

A) $750.00

This option is incorrect as $750.00 invested at 5 percent compounded annually for 20 years would yield a significantly lower future value than $15,000. The future value from this investment would be approximately $2,000, which is far below the target.

B) $5,653.34

This option is correct because it accurately represents the present value needed to accumulate $15,000 in 20 years at a 5 percent interest rate. The formula for present value shows that this amount, when compounded annually, will grow to the target amount.

C) $6,028.16

This choice is also incorrect, as investing $6,028.16 at 5 percent interest compounded annually for 20 years would result in a future value of approximately $17,000. This exceeds the target of $15,000, indicating that this is not the appropriate present value.

D) $7,500.00

Investing $7,500.00 at an interest rate of 5 percent compounded annually for 20 years would provide a future value of about $19,900. This sum is again above the desired amount of $15,000, making this option invalid for meeting the target.

G) $5

This option is incorrect as well, as an investment of only $5 at 5 percent interest compounded annually over 20 years would yield a trivial amount, far from the required $15,000. The future value would be negligible and insufficient for the goal.

Conclusion

The correct investment amount of $5,653.34 is essential to meet the future requirement of $15,000 in 20 years at a 5 percent annual interest rate compounded annually. All other options either fall short of or exceed the necessary amount, demonstrating their inadequacy in achieving the desired financial goal.