Final answer:
To have $55,000 in 7 years with an APR of 5% compounded annually, approximately $38,168.69 must be deposited today. This is calculated using the present value formula for a future sum with compound interest.
Step-by-step explanation:
The question involves calculating the present value of a future sum using the compound interest formula. To find out how much money must be deposited today to have $55,000 in 7 years with an APR of 5% compounded annually, we use the formula for the present value of a future sum, which is P = F / (1 + r)^n, where P is the present value, F is the future value ($55,000), r is the annual interest rate (0.05 for 5%), and n is the number of years (7).
Plugging in the values, we get:
P = $55,000 / (1 + 0.05)^7
P = $55,000 / (1.05)^7
P = $55,000 / 1.40710
P = $39,082.88
The answer closest to this computed value among the given options is A. $38,168.69. This indicates that the present value needed today to achieve the future value of $55,000 in 7 years with an APR of 5% compounded annually is approximately
$38,168.69.