Question

You borrow $2,000 for one year at an interest rate of 1% compounded each month. If this same sum of money can be borrowed for one year at an interest rate of 12% compounded annually, then which is the preferred alternative for the borrower?

Answer 1

The preferred alternative for the borrower is Scenario 2, which involves borrowing $2,000 for one year at an interest rate of 12% compounded annually, resulting in a total repayment amount of $2,240.

Step-by-step explanation:

To determine the preferred alternative, we need to compare the total amount of money that will be repaid in each scenario.

For Scenario 1: Borrowing $2,000 for one year at an interest rate of 1% compounded each month:

1. Calculate the monthly interest rate: 1% divided by 12 months = 0.08333%
2. Calculate the total amount after one year: $2,000 * (1 + 0.0008333)^12 = $2,024.25

For Scenario 2: Borrowing $2,000 for one year at an interest rate of 12% compounded annually:

1. Calculate the total amount after one year: $2,000 * (1 + 0.12) = $2,240

Comparing the two scenarios, it is clear that Scenario 2 is the preferred alternative for the borrower, as it results in a lower total repayment amount ($2,240) compared to Scenario 1 ($2,024.25).