Question

Paul and Frank each borrow $1,323 for 6 months.

Paul's loan uses the simple discount model while Frank's loan uses the simple interest model. The annual simple discount rate on Paul's loan is 13.9%.

What would the annual simple interest rate have to be on Frank's loan if their maturity values are the same?

Answer 1

1. Maturity value of Paul's simple discount Loan = Amount - Amount * interest rate * 6/12 = $1323

Maturity value of Paul's simple discount Loan = Amount - Amount * 13.90% * 0.50 = $1323

Maturity value of Paul's simple discount Loan = Amount * 0.9305 = $1323

Maturity value of Paul's simple discount Loan = Amount = $1421.82

2. Simple Interest Rate =

Maturity Value = Principal + principal * interest rate * Time

1421.82 = 1323 + 1323 * interest rate * 6/12

1421.82 = 1323 + 661.50 * interest rate

Interest rate = 14.94%