Question

Javier took out a loan for $2700 at 12% interest, compounded annually. If he makes yearly payments of $320, will he ever pay off the loan?

Answer 1

Answer :

He will not pay off the loan with the given yearly payment.

Explanation :

Since, the payment per period of a loan is,

$P=\frac{r(P.V.)}{1-(1+r)^{-n}}$

Where, P.V. is the principal amount,

r is the rate per period,

n is the number of periods,

Here, P.V. = $ 2700,

Annual rate = 12 % = 0.12

Since, the payment is paid yearly,

So, the rate per period, r = 0.12

Also, P = $ 320,

Thus, by substituting the values on the above formula,

$320=\frac{0.12(2700)}{1-(1+0.12)^{-n}}$

Since, this equation does not give the real value of n,

Hence, he will not pay off the loan with the given yearly payment.

Answer 2

He will never pay off the loan because it is increasing at 324 per year, for the first year and the interest will only increase which means 320 a year will not even make a dent in the loan