Question

If you want to buy a car, and you can afford a monthly payment of $400, how large of a loan can you get at 7.9% interest over 60 months(5 years)? Round your answer to the nearest dollar.

Answer 1

Solution:

We have the formula for EMI as below:

EMI = r*(PV)/(1 – (1+r)^(-n))

Where EMI is monthly payment or installment, PV is present value, r = rate per period, n = number of periods

We are given

EMI = 400

R = 7.9% annual

So, R = 7.9/12 = 0.658333333% monthly, that is

R = 0.006583

N = 60 months

EMI = r*(PV)/(1 – (1+r)^(-n))

400 = 0.006583*PV/(1 - (1+0.006583)^(-60)

400*(1 - (1+0.006583)^(-60))/0.006583 = PV

PV = 400*(1 - (1+0.006583)^(-60))/0.006583

PV = 400*0.325434/0.006583

PV = 19774.21

Required Answer = $19774