A recent engineering graduate intends to purchase a new car

A recent engineering graduate intends to purchase a new car. He plans to pay $2000 down and to finance the balance over a Cyear period. The maximum amount that he can repay each month is $200. What is the most expensive car that he can afford, assuming an interest rate of 12O/0 per year, compounded monthly and continuous compounding?

Solution

Formula to calculate EMI is given as follows:

EMI= P x r x ((1 + r)^n) / (((1+r)^n) -1)

Where,

EMI = every month instalments

r= rate of interest per month (eg : if interest rate per annum is 8% then it is calculated as 8/(12*100))

P =loan amount

n=duration in months

here, EMI = 200, r= 12/(12*100) = 0.01% per month, n = 48 months

200 = P * 0.01 * ((1+0.01)^24)/(((1+0.01)^24)-1)

200 = P * 0.01 * (1.01^24)/((1.01^24)- 1)

200 = P * 0.01 * 1.2697/0.2697

200 = P * 0.0470

P = 4255.31

Cost of the most expensive car that he can afford = down payment + loan amount taken

Cost of the most expensive car that he can afford = 2000 + 4255.31

Cost of the most expensive car that he can afford = $ 6255.31