Question

John takes out a loan for $11900 at 10% interest compounded monthly and is making payments of $116 a month. Calculate his remaining balance after 18 months.John's balance due after 18 months will be $The given answer is: 11574.55I need the breakdown of how to solve for this.

Answer 1

Given

Rate = 10% compunded monthly

Loan Amount , P = $11900

Making payment per month = %119

Find

Remaining balance after 18 months

Step-by-step explanation

Time period = 18/12 = 3/2 years

As we know

Amount =

`\begin{gathered} P(1+((R)/(12))/(100))^(12n) \\ 11900(1+((10)/(12))/(100))^{12*(3)/(2)} \\ 11900(1+((10)/(12))/(100))^(18) \\ 11900(1+(5)/(600))^(18) \\ 11900((121)/(120))^(18) \\ 13,817.2359 \end{gathered}`

john pays $16 per month

so, after 18 months , he pays

`116*18=2088`

therfore his remaining balance after 18 months = $ (13,817.2359 - 2088) = $ 11729

Final Answer

his remaining balance after 18 months = $ 11729