Question

Digital Access Inc. needs $323,640 in funds for a project. (Assume the loan term is one year.) a. With a compensating balance requirement of 7 percent, how much will the firm need to borrow? (Do not round intermediate calculations.) Amount to be borrowed $ b. Given your answer to part a and a stated interest rate of 17 percent on the total amount borrowed, what is the effective rate on the $323,640 actually being used? (Input your answer as a percent rounded to 2 decimal places.) Effective rate of interest %

Answer 1

Part a.

Let's assume the amount to be borrowed as X

Funds required by Digital Access: $323,640

Compensating balance requirement: 7%

This means that (1-7%) of X = $323,640

Solving for X,

X = $323,640 / (1-7%) = $323,640 / 0.93 = $348,000

Hence, the amount to be borrowed X = $348,000.

Calculation check -

Amount Digital Access needs from the loan amount = 93% * $348,00 = $323,640

Compensating balance requirement from the loan amount = 7% * $348,000 = $24,360

Part b.

To calculate the effective interest rate, one needs to keep in mind that the interest rate would be applicable on the entire loan amount i.e. $348,000 but Digital Access only needs $323,640 for the project as 7% is a compensating balance requirement for the bank providing the loan.

Stated interest rate on the loan amount = 17%

Loan amount = $348,000 (from part a)

Interest to be paid on the loan amount = 17% * $348,000 = $59,160

Effective interest amount on $323,640 = $59,160 (interest on the loan amount)

Effective interest rate on $323,640 = $59,160 / $323,640 = 18.28%

Effective interest rate on $323,640 being used is 18.28%

NB: No day / date convention has been provided, that's why the effective interest rate calculation has been done in the simplest manner.

Calculation check -

Effective interest amount on $323,640 being used = 18.28% * $323,640 = $59,161

Interest rate on the loan amount = $59,161 / $348,000 = 17%