Question

#5 Derek decides to buy a new car. The dealership offers him a choice of paying $548.00 per month for 5 years (with the first payment due next month) or paying some $28,871.00 today. He can borrow money from his bank to buy the car. What interest rate makes him indifferent between the two options? Submit Answer format: Percentage Round to: 3 decimal places (Example: 9.243%, % sign required. Will accept decimal format rounded to 5 decimal places (ex: 0.09243))

Answer 1

Interest rate =  0.05239 OR 5.239%

You can enter any of the two values

Explanation

Let ....... x % is the interest rate that makes him indifferent between the two options.

Annuity = 548 per month

Present value of annuity = 548 * [ 1 - (1+x )^-n ] / x = 28871

= 548 * [ 1 - (1 + x )^-60 ] / x = 28871

n = 5 Years * 12 = 60 months

For solving the above equation, use the excel function ......... = RATE(nper, pmt, pv)

nper = 60

pmt = 548

pv = - 28871

= RATE(60, 548, - 28871)

= 0.00436594

But we, have to express the interest rate in APR ( annual percentage rate) = 12 * 0.00436594 = 0.05239

OR 5.239%