Question

what interest rate would make it worthwhile to incur a compensating balance of $7,500 in order to get a 0.65-percent lower interest rate on a 2-year, pure discount loan of $150,000? (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.)

Answer 1

To calculate the interest rate that would make it worthwhile to incur a compensating balance, we need to compare the interest paid on the loan without the compensating balance to the interest paid on the loan with the compensating balance.

The interest rate that would make it worthwhile is approximately 1.30%.

To calculate the interest rate that would make it worthwhile to incur a compensating balance, we need to compare the interest paid on the loan without the compensating balance to the interest paid on the loan with the compensating balance.

Here are the steps:

1. Calculate the interest paid on the loan without the compensating balance:

• Loan amount: $150,000
• Interest rate: 0.65% (0.0065 as a decimal)

Interest paid = Loan amount × Interest rate × Time

Interest paid = $150,000 × 0.0065 × 2

Interest paid = $1,950

1. Calculate the interest paid on the loan with the compensating balance:

• Loan amount: $150,000 - $7,500 = $142,500
• Interest rate: ? (Unknown)

1. Set up a proportion to find the interest rate:

• Interest rate without compensating balance: Interest paid without compensating balance / Loan amount without compensating balance = $1,950 / $150,000 = 0.013
• Interest rate with compensating balance: Interest paid with compensating balance / Loan amount with compensating balance = ? / $142,500

0.013 = ? / $142,500

? = 0.013 × $142,500

? = $1,852.50

1. Rounded to 2 decimal places, the interest rate that would make it worthwhile to incur a compensating balance of $7,500 is approximately 1.30%.