Question

You bought a car and have to pay $500 monthly, for 36 months. How much did the car cost? The monthly interest rate is 1.7%. a. Assuming you first payment is at the end of this month b. Assuming your first payment is right away c. Assuming your first payment is in 12 months

Answer 1

Given about a car loan,

Monthly payment = $500

number of payments N = 36

monthly rate r = 1.7%

a). When first payment is at the end of the month, it is an ordinary annuity

Present value/cost in such case is

PV = PMT*(1 - (1+r)^-N)/r = 500*(1 - (1+0.017)^(-36))/0.017 = $13380.54

So, the car cost $13380.54

b). When first payment is right away, it is an annuity due

Present value/cost in such case is

PV = PMT*(1+r)*(1 - (1+r)^-N)/r = 500*1.017*(1 - (1+0.017)^(-36))/0.017 = $13608.01

So, the car cost $13608.01

c). When first payment is in 12 months, cost of car at the date of first payment is same as in case b

So, its cost now = cost at month 12/(1+r)^12 = 13608.01/1.017^12 = $11115.86

So, the car cost $11115.86