Question

Phil can afford $160 a month for 4 years for a car loan. If the interest rate is 4.3 percent (APR) compounded monthly, how much can he afford to borrow to purchase a car?

Answer 1

Monthly Payment = $160
Number of Payments = 48 (4 years)

Annual Interest Rate = 4.30%
Monthly Interest Rate = 4.30% / 12
Monthly Interest Rate = 0.35833%

Present Value of Monthly Payments = $160/1.0035833 + $160/1.0035833^2 + … + $160/1.0035833^47 + $160/1.0035833^48
Present Value of Monthly Payments = $160 * (1 - (1/1.0035833)^48) / 0.0035833
Present Value of Monthly Payments = $160 * 44.02662142
Present Value of Monthly Payments = $7,044.26

So, Phil can afford to buy a car worth $7,044.26 or $7,044.

Answer 2

Loan amount = Present value of future monthly payments = monthly payment * [1-(1+i)^-n]/i

i = interest rate per period

n = number of periods

=>

Loan amount = 160 * [1-(1+0.043/12)^-48]/(0.043/12)

= 7044.25 ........ans