Question

A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $2,500 per month for the next two years and then $3,000 per month for another two years after that. If the bank is charging customers 6.5 percent APR, how much would it be willing to lend the business owner?

Answer 1

Present value = $115,278.17

Step-by-step explanation:

Given data:

Monthly repay amount for 2 year = $2500

Monthly repay amount for another 2 year = $3500

APR =6%

monthly interest rate = 6.50/12 = 0.54167%

Present value is calculated as

Present value
`= (monthly payment)/((1 + monthly rate)^n)`

Present value
`= (2500)/((1 + 0.54167\%)^1) +(2500)/((1 + 0.54167\%)^2) +........ + (2500)/((1 + 0.54167\%)^(24)) +  (3000)/((1 + 0.54167\%)^(25)) + ...... + (3000)/((1 + 0.54167\%)^(48))`

Present value
`= 2500* ((1-((1)/(1.0054167))^(24)))/(0.0054167) + 3000* ((1-((1)/(1.0054167))^(24)))/(0.0054167)`

Present value = $115,278.17