Question

You bought a car and have to pay $500 monthly, for 36 months. How much did...

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

Homework Answers

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

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