Question

A homeowner is financing the cost of new windows. Two lenders have approved the homeowner for a $12,000 loan. The terms of each loan are:

Offer 1: 4.5% annual simple interest, with a total account balance of $14,430 after a 54-month term
Offer 2: 3.75% annual interest compounded monthly for a 66-month term

Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest penny.

A. $204.88
B. $313.98
C. $767.12
D. $795.34

Answer 1

To find the difference in the account balances at the end of the loan terms, calculate the final balance for each loan offer using the formulas for simple interest and compound interest. The difference in the account balances is $313.98.

Step-by-step explanation:

To find the difference in the account balances at the end of the loan terms, we need to calculate the final balance for each loan offer.

For offer 1, we can use the formula for simple interest:

Final Balance = Principal + Principal * Interest Rate * Time

Plugging in the values, we get: Final Balance = $12,000 + $12,000 * 0.045 * 4.5 = $14,430

For offer 2, we can use the formula for compound interest:

Final Balance = Principal * (1 + Interest Rate/Number of Compounding Periods)^(Number of Compounding Periods * Time)

Plugging in the values, we get: Final Balance = $12,000 * (1 + 0.0375/12)^(12 * 66) = $14,721.98

The difference in the account balances is: $14,721.98 - $14,430 = $291.98

Therefore, the correct answer is B. $313.98.