Question

Suppose that you borrow $14,000 for five years at 6% toward the purchase of a car. Find the monthly payment and the total interest for the loan.

Answer 1

We have to calculate the monthly payments (number of subperiods per year n = 12) for a loan of $14,000 (P = 14000) for five years (t = 5) at an interest rate of 6% (r = 0.06).

We can use the annuity formula to calculate the monthly payment (PMT) as:

`\begin{gathered} \text{PMT}=(P((r)/(n)))/(\lbrack1-(1+(r)/(n))^(-nt)\rbrack) \\ \text{PMT}=(14000\cdot((0.06)/(12)))/(\lbrack1-(1+(0.06)/(12))^(-12\cdot5)\rbrack) \\ \text{PMT}=(14000\cdot0.005)/(\lbrack1-1.005^(-60)\rbrack) \\ \text{PMT}\approx(14000\cdot0.005)/(1-0.74137) \\ \text{PMT}\approx(70)/(0.25863) \\ \text{PMT}\approx270.66 \end{gathered}`

Answer: the monthly payments will be $270.66