Question

Problem 5-24 Present Value of Multiple Annuities (LG5-4)

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.)

Answer 1

Interest Rate = 10.25%

From Year 1 to Year 3,

Monthly Payment = $2,200

Calculating Present Value,

PV = [FV = 0,T = 36, PMT = 2200, I = 0.1025]

Present value = $67,933.34

From Year 4 to Year 5,

Monthly payment = $1,200

Calculating Present Value,

PV = [FV = 0,T = 24, PMT = 1200, I = 0.1025]

Present value(end of Year 3) = $25,940.11

Present Value = 25,940.11/(1 + 0.1025/12)³⁶

Present Value = $10,432.38

So,

Amount of Loan = 67,933.34 + 10,432.38

Amount of Loan = $78,365.72