Question

Brady took out a loan for $2800 at an 18% APR, compounded monthly, to buy a computer. If he will make monthly payments of $201.50 to pay off the loan, how many total payments will he have to make?

Answer 1

Answer:

Brady will have to make approximately 16 payments.

Step-by-step explanation:

Monthly Payment formula is:   $M= P[\frac{r}{1-(1+r)^-^n}]$

where,  $M=$ Monthly payment,  $P=$ Loan amount,  $r=$ Annual interest rate and $n=$ total number of periods.

Here,   $M= 201.50, P= 2800$

$r= 18\% yearly = (\frac{0.18}{12}) monthly = 0.015$

Plugging these values into the above formula.....

$201.50=2800[\frac{0.015}{1-(1+0.015)^-^n}]\\ \\ 201.50=\frac{42}{1-(1.015)^-^n}\\ \\ 1-(1.015)^-^n=\frac{42}{201.50}\\ \\ 1-(1.015)^-^n=0.208\\ \\ (1.015)^-^n =1-0.208\\ \\ (1.015)^-^n=0.792\\ \\ log(1.015)^-^n=log(0.792)\\ \\ -n*log(1.015)=log(0.792)\\ \\ -n=\frac{log(0.792)}{log(1.015)}=-15.66\\ \\ n=15.66 \approx 16$

So, he will have to make approximately 16 payments.

Answer 2

The answer here is 16 according to apex and my brain