Question

You are borrowing money to buy a car. If you can make payments of $300 per month starting one month from now at an interest rate of 4%, how much will you be able to borrow for the car today if you finance the amount over four years?

A. $6,358.54
B. $13,067.62
C. $15,587.88
D. $13,286.65

Answer 1

d) Amount to be borrowed = $13,286.65

Step-by-step explanation:

The amount to be borrowed is equal to the present value of the payment annuity of $300 per month for 4 years at an interest rate of 4%.

The monthly $300 payment represents an installment which will cover both the principal and interest that will accrue over the life of the loan. This series of annual payment is called an annuity.

The present value of annuity is computed using this formula:

PV of Annuity = installment × (1- (1 + r)^(-n))/r

equal installment- 300, r= 4%/12 = 0.33% , n= 4 × 12 = 18

The Present value is computed as follows:

PV = 300 × (1- (1.0033)^(-4× 12))/0.0033)

= 300 × 44.28

= $13,286.65