Question

An amount of $44,000 is borrowed for 12 years at 3.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

A) $63,585.55
B) $56,324.80
C) $59,347.20
D) $67,812.40

Answer 1

Calculating the future value of a loan using the compound interest formula results in a payoff amount of approximately $66,420.64 after 12 years, which is not listed in the provided answer choices.

Step-by-step explanation:

To solve the problem, we need to calculate the future value of the amount of $44,000 borrowed for 12 years at 3.5% interest, compounded annually. The formula for the future value, FV, of an investment is given by:

FV = P × (1 + r)^n

Where:

• P is the principal amount (the initial amount of money)
• r is the annual interest rate (decimal)
• n is the number of years the money is invested or borrowed for

In this case:

• P = $44,000
• r = 3.5% = 0.035 (as a decimal)
• n = 12 years

Plugging the values into the formula, we get:

FV = $44,000 × (1 + 0.035)^12

FV = $44,000 × (1.035)^12

FV = $44,000 × 1.50956

FV ≈ $66,420.64

Therefore, the correct answer is not listed among the options provided. The borrower must pay approximately $66,420.64 at the end of the 12-year period to pay off the loan in full.