Question

Determine the actual annual interest rate on a $100,000 line of credit with an annual percentage rate of 10% compounded monthly. The bank requires that a 5% compensating balance be placed in an interest-bearing account that pays an annual percentage rate of 1.5% compounded monthly. The average daily balance is anticipated to be $75,000, excluding the compensating balance and interest due on the line of credit.

Answer 1

The Average Daily balance is 75000

Therefore, the interest on the 75000 @ 10% compunded monthly is calculated using the formual :

A= P(1+r/n)^nt where A is the final amount including interest , P(=75000) is the principal, r(=10%) is the rate of interest per annum, n(=12) is the compounding per year and t is the time period required ( 1 year)

75000*(1+0.1/12)^12

This solves to a amount that is inclusive of interest = 82,853

Therefore , we reduce the initial amount of 75,000 from this figure to get 7,853

This is the interest cost on the line of credit based on avg. daily utilisation of 75,000.

The actual Interest incurred by the borrower is 7,853

But as the bank requires a compensating 5% deposit with an interest rate of 1,5% per annum, compounded monthly, the above interst outgo can be reduced by the interest earnings on 5000 ( 5% of 100,000)

Using the same formula as above we arrive at an interest earning of 50.23 per annum

Therefore net Interest expense would be 7,853 less 50 i.e. 7,800