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

Answer:

Present value = $115,278.17

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 $= \frac{monthly payment}{(1 + monthly rate)^n}$

Present value $= \frac{2500}{(1 + 0.54167\%)^1} +\frac{2500}{(1 + 0.54167\%)^2} +........ + \frac{2500}{(1 + 0.54167\%)^{24}} +  \frac{3000}{(1 + 0.54167\%)^{25}} + ...... + \frac{3000}{(1 + 0.54167\%)^{48}}$

Present value $= 2500\times \frac{(1-(\frac{1}{1.0054167})^{24})}{0.0054167} + 3000\times \frac{(1-(\frac{1}{1.0054167})^{24})}{0.0054167}$

Present value = $115,278.17