Question

Jane wanted to buy a new set of furniture for her living room. The furniture cost $1400. She takes out an add-on loan for 2 years at an annual interest rate of 18%. How much will Jane’s annual payments be? As well how much interest will Jane end up paying?

Answer 1

GIVEN:

We are told that Jane wanted to buy a set of furniture for $1400. The terms are, 2-year loan at the rate of 18% per annum.

Required;

To determine how miuch her annual payment will be. Also, how much interest will she be paying?

Step-by-step solution;

We begin b y identifying the following;

$\begin{gathered} Principal=1400 \\ Rate(r)=0.18\text{ }(18\%) \\ Time(N)=2 \\ Period(K)=12 \end{gathered}$

The monthly payment will now be determined by the formula below;

$P=\frac{PMT(1-(1+\frac{r}{K})^{-N\times K}}{\frac{r}{K}}$

Now we substitute values;

$\begin{gathered} 1400=\frac{PMT(1-(1+\frac{0.18}{12})^{-2\times12}}{\frac{0.18}{12}} \\ \\ 1400=\frac{PMT(1-(1+0.015)^{-24}}{0.015} \\ \\ 1400=PMT(20.0304053663) \\ \\ \frac{1400}{20.0304053663}=PMT \\ \\ PMT=69.8937427575 \end{gathered}$

Therefore, the monthly payment will be $69.89 (approximately).

Therefore, annual payments will be;

$\begin{gathered} Annual\text{ }payment=69.89\times12 \\ \\ Annual\text{ }payment=\text{\ }838.68 \end{gathered}$

To determine her interest payment we calculate her total payments as follows;

$\begin{gathered} Total\text{ }payments=69.89\times24 \\ \\ Total\text{ }payments=1677.36 \end{gathered}$

The interest payment therefore would be;

$\begin{gathered} Interest=Total\text{ }payment-Initial\text{ }amount \\ \\ Interest=1677.36-1400 \\ \\ Interest=277.36 \end{gathered}$

Therefore;

ANSWER:

(a) Annual payment = $838.68

(b) Interest paid = $277.36