Two stores are offering a fridge and washing machine combo package. Store A offers a monthly payment of \(\text{R}\,\text{350}\) over \(\text{24}\) months. Store B offers a monthly payment of \(\text{R}\,\text{175}\) over \(\text{48}\) months.

If both stores offer \(\text{7,5}\%\) interest, which store should you purchase the fridge and washing machine from if you want to pay the least amount of interest?

To calculate the interest paid at each store we need to first find the cash price of the fridge and washing machine.

Store A:

\begin{align*}
A & = \text{350} \times \text{24} = \text{8 400}\\
P & = ? \\
i & = \text{0,075} \\
n & = 2 \\\\
A & = P(1 + in) \\
\text{8 400} & = P(1 + (\text{0,075})(2)) \\
\frac{\text{8 400}}{\text{2,15}} & = P\\
P & = \text{R}\,\text{3 906,98}
\end{align*}

Therefore the interest is \(\text{R}\,\text{8 400} - \text{R}\,\text{3 906,98} = \text{R}\,\text{4 493,02}\)

Store B:

\begin{align*}
A & = \text{175} \times \text{48} = \text{8 400}\\
P & = ? \\
i & = \text{0,075} \\
n & = 4 \\\\
A & = P(1 + in) \\
\text{8 400} & = P(1 + (\text{0,075})(4)) \\
\frac{\text{8 400}}{\text{4,3}} & = P\\
P & = \text{R}\,\text{1 953,49}
\end{align*}

Therefore the interest is \(\text{R}\,\text{8 400} - \text{R}\,\text{1 953,49} = \text{R}\,\text{6 446,51}\)

If you want to pay the least amount in interest you should purchase the fridge and washing machine from store A.

Tlali wants to buy a new computer and decides to buy one on a hire purchase agreement. The computers cash price is \(\text{R}\,\text{4 250}\). He will pay it off over \(\text{30}\) months at an interest rate of \(\text{9,5}\%\) p.a. An insurance premium of \(\text{R}\,\text{10,75}\) is added to every monthly payment. How much are his monthly payments?

\begin{align*}
P & = \text{4 250} \\
i & = \text{0,095} \\
n & = \frac{30}{12} = \text{2,5}
\end{align*}

The question does not mention a deposit, therefore we assume that Tlali did not pay one.

\begin{align*}
A & = P\left(1 + in\right) \\
A & = \text{4 250}\left(1 + \text{0,095}\times \text{2,5}\right) \\
& = \text{5 259,38}
\end{align*}

The monthly payment is:

\begin{align*}
\text{Monthly payment } & = \frac{\text{5 259,38}}{36} \\
& = \text{146,09}
\end{align*}

Add the insurance premium: \(\text{R}\,\text{146,09} + \text{R}\,\text{10,75} = \text{R}\,\text{156,84}\)

Richard is planning to buy a new stove on hire purchase. The cash price of the stove is \(\text{R}\,\text{6 420}\). He has to pay a \(\text{10}\%\) deposit and then pay the remaining amount off over \(\text{36}\) months at an interest rate of \(\text{8}\%\) p.a. An insurance premium of \(\text{R}\,\text{11,20}\) is added to every monthly payment. Calculate Richard's monthly payments.

\begin{align*}
P & = \text{6 420} - (\text{0,10})(\text{6 420}) = \text{5 778} \\
i & = \text{0,08} \\
n & = \frac{36}{12} = \text{3}
\end{align*}

Calculate the accumulated amount:

\begin{align*}
A & = P\left(1 + in\right) \\
A & = \text{5 778}\left(1 + \text{0,08}\times \text{3}\right) \\
& = \text{7 164,72}
\end{align*}

Calculate the monthly repayments on the hire purchase agreement:

\begin{align*}
\text{Monthly payment } & = \frac{\text{7 164,72}}{36} \\
& = \text{199,02}
\end{align*}

Add the insurance premium: \(\text{R}\,\text{199,02} + \text{R}\,\text{11,20} = \text{R}\,\text{210,22}\)