Question

A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $2,200 per month for the next three years and then $1,200 per month for two years after that. If the bank is charging customers 10.25 percent APR, how much would it be willing to lend the business owner? (Do not round intermediate calculations and round your final answer to 2 decimal places.) What is the present value?

Answer 1

Present value of the first set pf payments for three years is $67,933.34 calculated as of an annuity as follows:

Discounted value of the next set of payments, at the beginning of the two year term is $25,940.11 calculated as follows:

Present value of this amount as on now is calculated as

PV= FV/(1+r)^n

Where FV is the value after 3 years, r= rate of interest (10.25%) and n= term No. of months ie., 36)

Therefore, PV of second set of payments= $25,940.11/(1+0.1025)^36= $25,940.11/1.35824598= $19,098.24

Loan amount= Total of present values of the 2 sets of payments

=$67,933.34+ $19,098.24 = $87,031.58