Harper Engine Company needs $611,000 to take a cash discount of 2.50/10, net 75.

Question

Harper Engine Company needs $611,000 to take a cash discount of 2.50/10, net 75. A banker will loan the money for 65 days at an interest cost of $16,200.

What is the effective rate on the bank loan?

How much would it cost (in percentage terms) if Harper did not take the cash discount but paid the bill in 75 days instead of 10 days?

If another banker requires a 10 percent compensating balance, how much must Harper borrow to end up with $611,000?

What would be the effective interest rate in part d if the interest charge for 65 days were $10,600?

What is the effective rate on the bank loan?

How much would it cost (in percentage terms) if Harper did not take the cash discount but paid the bill in 75 days instead of 10 days?

If another banker requires a 10 percent compensating balance, how much must Harper borrow to end up with $611,000?

What would be the effective interest rate in part d if the interest charge for 65 days were $10,600?

Explanation / Answer

a) Effective rate on the bank loan = (1+ interest cost/Amount Borrowed)^(365/65) -1

Effective rate on the bank loan = (1+16200/611000)^(365/65) - 1

Effective rate on the bank loan = 15.83%

b) Cost of Cash Discount = (1 + 2.5/(100-2.5))^(365/65) - 1

Cost of Cash Discount = 15.27%

c) Harper borrow to end up   = 611000/(1-10%)

Harper borrow to end up = 678,888.89

d) Effective interest rate = (1+ interest cost/Amount Borrowed)^(365/65) -1

Effective interest rate =  (1+10600/611000)^(365/65) - 1

Effective interest rate = 10.14%

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