Question

Just a Little Bit Each Month - You’ve recently finished your MBA at the Darnit School. Naturally, you must purchase a new BMW immediately. The car costs about $36,000. The bank quotes an interest rate of 15 percent APR for a 72-month loan with a 10 percent down payment. You plan on trading the car in for a new one in two years. What will your monthly payment be? What is the effective interest rate on the loan? What will the loan balance be when you trade the car in?

Answer 1

So the terms of the loan were ,

Downpayment = 10%

APR rate = 15%

Time of loan = 72 months .

So the price of the BMW is 36,000

The down payment is = 10% or 0.10*36000 = 3600

The amount of Loan would be 36000-3600 = 32400

Now

The Amortised monthly payments will be

Payments = (principal x(i/m ) / (1-(1+(i/m)) ^ -mt

Where m is the no of payments in a year

And the t is the time frame of the loan

So We calculate as

M.Payments = ( 32400x (0.15/12) ) / (1-(1+(0.15/12)) ^ -72

= 685.0984

The Car is planned to be sold in a 2year period

SO ,

Total Payments made in 24 months = 685.0984 * 24 = 16442.36

Total accrued interest paid = 8658.96

Effective Interest rate per year = (8658.965/ 32400) / 2 * 100 = 13.37% pa

Loan balance at end of 2 years .

= Initial balance + Accrued intersts – Total paid instalments

= 32400 +8658.96 – 16442.36

= 24616.61