Question

Brenna wants to buy a car that is available at two dealerships. The price of the car is the same at both dealerships. Best Buggies would let her make quarterly payments of $2,250 for 5 years at a quarterly interest rate of 3.82 percent. Her first payment to Best Buggies would be due immediately. If California Cars would let her make equal monthly payments of $920 at a monthly interest rate of 1.35 percent and if her first payment to California Cars would be in 1 month, then how many monthly payments would Brenna need to make to California Cars?  Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00)

Answer 1

Best Buggies

Payment = P = $2250

Number of periods = n = 5*4 = 20

Interest rate r = 3.82% quarterly

First payment is made now

=> PV = P + P[1-(1+r)^-(n-1)]/r = 2250 + 2250(1 - 1.0382^-19)/0.0382 = $32258.39

California Cars

Payment = P = $920

Number of periods = n

Interest rate r = 1.35% monthly

First payment is made at end of first month

=> PV = P[1-(1+r)^-n]/r = 920(1 - 1.0135^-n)/0.0135

This is equal to $32258.39

=> 920(1 - 1.0135^-n)/0.0135 = 32258.39

=> n = 47.82 months