Interest

Hannah borrowed £600 from her friend for a year at an interest rate of 5%. What is the simple interest?

Solution

The information given is

$$\begin{gathered} P=\pounds 600 \\ T=1year \\ R=5\% \\ SI=? \end{gathered}$$

The simple interest can be calculated via the formula,

$$\begin{gathered} SI=PRT \\ =600\times \frac{5}{100}\times 1 \\ =600\times 0.05 \\ =\pounds 30 \end{gathered}$$

I borrowed £20,000 from the bank for three years at an interest rate of 10% per annum. How much will I pay back at the end of the three years?

Solution

The first thing we need to do is list out all information given to us.

$$\begin{gathered} P=\pounds 20000 \\ T=3years \\ R=10\% \\ Amounttobepaidback=? \end{gathered}$$

The formula to find the amount is given by

$Amount=P+SI$

To find the amount, we must first calculate the simple interest using the simple interest formula, which is,

$$\begin{gathered} SI=PRT \\ =20000\times \frac{10}{100}\times 3 \\ =20000\times 0.1\times 3 \\ =\pounds 6000 \end{gathered}$$

We will now find the amount which is the sum of the principal and the simple interest.

$$\begin{gathered} Amount=20000+6000 \\ =\pounds 26000 \end{gathered}$$

The simple interest on an amount of money is £1000. The Percentage interest rate is 4% and it is to be paid after four years. What is the principal amount?

Solution

In the question, we are given the simple interest, the interest rate, and the time.

$$\begin{gathered} SI=\pounds 1000 \\ R=4\% \\ T=4years \\ P=? \end{gathered}$$

The simple interest formula is given by

$SI=PRT$

We substitute the values we have in the simple interest formula,

$$\begin{gathered} 1000=P\times \frac{4}{100}\times 41000 \\ =P\times 0.04\times 41000 \\ =0.16P \end{gathered}$$

We need to isolate P and make it the subject of the formula so we can find its value by dividing both sides of the equation by 0.16. We get:

$$\begin{gathered} \frac{1000}{0.16}=\frac{0.16P}{0.16} \\ P=\frac{1000}{0.16} \\ P=\pounds 6250 \end{gathered}$$

Someone deposited £10,000 to his savings account to earn an interest of 10% every year for five years. How much will be withdrawn at the end of the fifth year?

Solution

The information given in the question is below.

$$\begin{gathered} P=\pounds 10000 \\ R=10\% \\ n=5years \\ Amountafter5years=? \end{gathered}$$

The compound interest formula is:

$$\begin{gathered} Amountafternyears=Principal\times {(1+rate)}^n \\ =10000\times {\left[1+\frac{10}{100}\right]}^5 \\ =10000\times {\left[1.1\right]}^5 \\ =10000\times 1.61051 \\ =\pounds 16105.1 \end{gathered}$$

If you are to get £20,000 after five years at an interest rate of 10%, what is the principal amount you invested?

Solution

The information given in the question is below.

$$\begin{gathered} Amountafter5years=\pounds 20000 \\ Rate=10\% \\ n=5years \\ Principal=? \end{gathered}$$

The compound interest formula is,

$Amountafternyears=Principal\times {\left(1+rate\right)}^n$

What we are going to do is substitute the known values and solve for the unknown.

$$\begin{gathered} 20000=P\times {\left(1+\frac{10}{100}\right)}^{5}20000 \\ =P\times {(1+0.1)}^{5}20000 \\ =P\times {1.1}^{5}20000 \\ =1.61P \end{gathered}$$

We have to make P the subject of the formula and to do that, we will divide both sides of the equation by 1.61.

$$\begin{gathered} \frac{20000}{1.61}=\frac{1.61P}{1.61} \\ P=\frac{20000}{1.61} \\ P=\pounds 12422.36 \end{gathered}$$