Question

Up-Front Bank uses discount loans for all its customers who want​ one-year loans. ​ Currently, the bank is providing​ one-year discount loans at 7.9%.

a) What is the effective annual rate on these​ loans?

b) If you were required to repay $210,000 at the end of the loan for one​ year, how much would the bank have given you at the start of the​ loan?

Answer 1

(a)

Effective interest rate on discount loan formula = loan Discount rate/(1-Discount rate)

Loan Discount rate = 7.9% or 0.079

Effective interest rate = 0.079/(1-0.079)

0.08577633008 or 8.58%

So, effective interest rate on diacoudi loan is 8.58%

(B)

Required amount payable after 1 year for loan = $210000

It means $210,000 loan given at 7.9% discount

Amount given by bank = Amount of loan *(1-discount rate)

= 210,000*(1-0.079)

$193,410

So, bank would have given $193,410 at start of loan.