To the nearest $0.01, how much money should be invested now to have a balance of $15,000 in 20 years if the account earns 5 percent annual interest, compounded annually (no other deposits/withdrawals)?

Rationale

$5,653.34

To determine how much money should be invested now to achieve a balance of $15,000 in 20 years at an annual interest rate of 5 percent, compounded annually, we can use the formula for the present value of a future sum. The present value is calculated as ( PV = frac{FV}{(1 + r)^n} ), where ( FV ) is the future value, ( r ) is the interest rate, and ( n ) is the number of years. Plugging in the values gives us approximately $5,653.34.

A ($750.00) YOUR ANSWER

Investing $750.00 at a 5 percent interest rate compounded annually for 20 years would yield significantly less than $15,000. Using the present value formula, this amount would grow to only about $1,985.92, which is far below the target.

B ($5,653.34) CORRECT

This is the correct answer, as explained. Investing this amount at a 5 percent interest rate compounded annually for 20 years will correctly yield a future value of $15,000.

C ($6,028.16) YOUR ANSWER

Investing $6,028.16 at 5 percent interest compounded annually for 20 years would also fall short of the $15,000 target. This amount would grow to approximately $17,102.82, which is more than necessary; hence it’s not the required investment.

D ($7,500.00) YOUR ANSWER

Investing $7,500.00 at 5 percent interest compounded annually for 20 years would yield about $19,896.54. This amount exceeds the desired balance, indicating it is not the correct present value needed to reach $15,000.

Conclusion

To achieve a future balance of $15,000 in 20 years with a 5 percent annual interest rate compounded annually, an investment of approximately $5,653.34 is required. Other options either do not meet the target or exceed it, demonstrating the need for precise calculations in financial planning.

To the nearest $0.01, how much money should be invested now to have a balance of $15,000 in 20 years if the account earns 5 percent annual interest, compounded annually (no other deposits/withdrawals)?

$5,653.34

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