Question

A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $900 per month for the next two years and then $1,800 per month for three years after that. If the bank is charging customers 8.5 percent APR, how much would it be willing to lend the business owner? (Round your answer to two decimal places.)

Answer 1

Hi

Here first 2 years payment C = $900

rate r = 8.5%/12

time t = 2 years = 24 months

Loan amount will be present value of future payments

Present Value of first 2 years payment = (C/r)*(1-(1+r)^-t)

= (900/0.71%)*(1-(1+0.71%)^-24)   

= (900/0.71%)*(1-0.84)

= 127058.82*0.16

=$19,799.51

After that monthly payment = $1800

So present Value of next 3 years payment = (1800/0.71%)*(1-(1+0.71%)^-36) / (1+0.71%)^24

=254,117.65*0.22/1.185

=$48,135.11

Hence the amount that willing to be lend today = 19799.51 + 48135.11 = $67,934.62

Thanks