Simple Interest

Find the simple interest on £5000 with a percentage increase of 5% over 4 years.

Solution

To find the simple interest, we will use the simple interest formula below.

$SI=PRT$

From the question, we have

We will now substitute the values we have in the formula,

$SI=5000\times \frac{5}{100}\times 4=\pounds 1000$.

This means that over 4 years, there will be an increase of £1000.

Calculate the simple interest earned after 2 years on £5000 at an interest rate of 5%.

Solution

Recall that the formula for calculating simple interest is

$SI=PRT$

Let’s list out the information given,

$$\begin{gathered} T=2years \\ P=\pounds 5000 \\ R=5\% \\ SI=? \end{gathered}$$

Let’s substitute the values in the simple interest formula

$SI=5000\times \frac{5}{100}\times 2=5000\times 0.05\times 2=\pounds 500$.

If the simple interest on £300 over 2 years is £10, what is the rate?

Solution

Let’s first identify what we know and what we don’t know.

We know that

$$\begin{gathered} P=\pounds 300 \\ T=2YEARS \\ SI=\pounds 10 \\ R=? \end{gathered}$$

We don’t know the rate $R$ of the principal amount at the end of 5 months.

Recall the simple interest formula

$SI=PRT$

We can just go ahead and use the formula for the rate derived earlier or we can directly substitute into the simple interest formula. Let's substitute directly.

$$\begin{gathered} 10=300\times R\times 5 \\ 10=600R \end{gathered}$$

Divide both sides by 600 to get,

$$\begin{gathered} \frac{10}{600}=\frac{600R}{600} \\ R=0.0167 \end{gathered}$$

This is not our final answer because the rate we got is a decimal. The rate should be in percentage and to get it in percentage, we will have to multiply by 100.

$R=0.0167\times 100=1.67\%$.

Find the principal invested if £170 of interest was earned in 2 years at an interest rate of 4%.

Solution

Let’s first list what we know and what are we looking for.

$$\begin{gathered} P=? \\ SI=\pounds 170 \\ T=2years \\ R=4\%=\frac{4}{100}=0.04 \end{gathered}$$

We are looking for the principal amount. We can substitute the values we have in the simple interest formula and solve for $P$ or we can use the formula for $P$derived earlier.

We will use the formula derived earlier.

$P=\frac{SI}{RT}=\frac{170}{2}\times 0.04=\frac{170}{0.08}=\pounds 2125$

Find the rate if a principal of £8000 earned £3700 interest in 4 years.

Solution

As usual, we will list what we have. Stating what we have makes everything clearer.

$$\begin{gathered} R=? \\ P=\pounds 8000 \\ SI=\pounds 3700 \\ T=4years \end{gathered}$$

Let us use the formula for the rate that was derived earlier.

$R=\frac{SI}{PT}=\frac{3700}{8000\times 4}=\frac{3700}{32000}=0.1156$

Remember that the rate is always in percentage. So, we have to convert to a percentage by multiplying by 100.

$$\begin{gathered} R=0.1156\times 100 \\ R=11.56\% \end{gathered}$$

So the rate is 11.56%.

Find the amount and the simple interest earned on £550 over 3 years at an interest rate of 2%.

Solution

Let’s state what we know and what we are looking for.

$$\begin{gathered} Amount\left(A\right)=? \\ SI=? \\ P=\pounds 550 \\ T=3years \\ R=2\% \end{gathered}$$

We are asked to find the amount and the simple interest. We have to find the simple interest first before we can find the amount.

$SI=PRT=550\times \frac{2}{100}\times 3=\pounds 33$

The amount is the sum of the simple interest and the principal amount, thus

$Amount\left(A\right)=SI+P=33+550=\pounds 583$