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

- A small business owner visits her bank and states she can repay $900 per month for the next two years and then $1,800 per month for three years after that.

First, Calculating the Present Value today of payment made for the next 2 years:-

Where, C= Periodic Payments = $900

r = Periodic Interest rate = 8.5%/12 = 0.708333%

n= no of periods = 2 years*12 =24

Present value today of payment made for the next 2 years = $19,799.51

- Now, for the last 3 years periodic payment first we will calculate its Present value at the end of year 2 and then by using discounting method computing it back to Present value today:-

Where, C= Periodic Payments = $1800

r = Periodic Interest rate = 8.5%/12 = 0.708333%

n= no of periods = 3 years*12 =36

m = no of periods of discounting = 2 years*12 = 24

Present value today of payment made for the last 3 years = $48,135.11

Total present value = $48,135.11 + $19,799.51

= $67,934.62

So, Bank can lend to the business owner is $67,934.62