Question

Discount loan.  ​Up-Front Bank is now offering a​ two-year discount loan for 10.3%. Working​ backwards, what are the available funds at the start of the loan and the implied balance at the end of the first year if the total​ lump-sum repayment at the end of the second year is $430,000​? What is the EAR of this​ loan?

What are the available funds at the start of the loan if the total​ lump-sum repayment at the end of the second year is $430,000​?

Answer 1

Discount loan is the one in which interest and other charges are deducted from the loan amount at the time of loan is given at the given discount rate.

Amount of repayment at the end of year 2 = $430,000

Discount rate = 10.3% per year

Time period = 2 years

The available funds at the start of the loan = Amount of repayment at the end of year 2 * (1- discount rate) *(1-discount rate)

= $430,000 * (1-10.3%) (1-10.3%)

= $345,981.87

The available funds at the end of year one of the loan = the available funds at the start of the loan / (1- discount rate)

= $430,000 / (1-10.3%)

= $385,710

EAR of this loan = ($430,000/$345,981.87)^(1/2) -1 = 0.1148 or 11.48%