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

Brady will have to make approximately 16 payments.

Explanation:

Monthly Payment formula is:
`M= P[(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 = ((0.18)/(12)) monthly = 0.015`

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

`201.50=2800[(0.015)/(1-(1+0.015)^-^n)]\\ \\ 201.50=(42)/(1-(1.015)^-^n)\\ \\ 1-(1.015)^-^n=(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=(log(0.792))/(log(1.015))=-15.66\\ \\ n=15.66 \approx 16`

So, he will have to make approximately 16 payments.