Question

Susan took out a personal loan for $3,500 at an interest rate of 13% compounded monthly. she made arrangements to pay the loan off in 3 years. what will her monthly payment be?

Answer 1

If a loan has an interest which is compounded monthly, this means that n= 12. The rate will have a monthly interest of 13% per month. Since she is going to pay the loan off in 3 years, this would mean that her monthly payment would be $100 plus the interest per month of 13% which is $468. Therefore, the total monthly payment is $568. Hope this answer helps.

Answer 2

The monthly payment for this ordinary annuity is 117.88.

Further Explanation:

Annuity: It is a type of recurring payment which needs to be paid for the loan taken by someone. These payments include the principal amount of loan and the rate of interest for that period. At the end of the annuity payments, the interest to be paid becomes zero, and the full amount of principal is also paid by then thus resulting it to be the last payment.

The formula for computing annuity payments is:

$\begin{aligned}Annuity\:Payment\:(P)&=\:\dfrac{r\times{PV}}{1-(1+r)^{-n}}\\\\Where\:P&=Annuity\:Payment\:for\:the\:Period\\r&=\:Rate\:per\:Period\\PV&=Present\:Value\\n&=No.\:of\:Payments \end{aligned}$

Computation of monthly payment of Susan:

$\begin{aligned}P&=\dfrac{\dfrac{0.13}{12}\times\ 3,500}{1-\left (1+\left (\dfrac{0.13}{12}\right)^{-35}\right)}\\P&=\dfrac{0.0108\times\ 3,500}{1-1+0.0108)^{-36}}\\P&=\dfrac{\ 37.8167}{1-0.6792}\\P&=\ 117.88.\end{aligned}$

Therefore, the monthly payment of Susan is $117.88.

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Answer details:

Grade: Senior School

Subject: Finance

Chapter: Time Value of Money

Keywords: Annuity payments, monthly payments, personal loan, of, $3500, interest rate 13%, three years loan, recurring payments, for a period of time, till, payment, becomes, zero, includes principal, and interest, payment by Susan, annuity payment formula, annuity factor, table, at the end, of the year, at the beginning, of the year.