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

Explanation

Time period = 18/12 = 3/2 years

As we know

Amount =

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

john pays $16 per month

so, after 18 months , he pays

$116\times18=2088$

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

Final Answer

his remaining balance after 18 months = $ 11729