Simple Interest

Interest is either earned when we deposit money into a bank or paid when we borrow money. Simple interest is calculated using a straightforward formula that considers the principal amount, the interest rate, and the time for which the money is deposited or borrowed.

Formula for Simple Interest

The formula for simple interest is:

I = \frac{P \times R \times T}{100}

Where:

  • I = Simple interest earned or paid
  • P = Principal amount (money deposited or borrowed)
  • R = Rate of interest (as a percentage, e.g., 5%, 12%, etc.)
  • T = Time (in years)

Let’s look at some examples.

Examples

Example 1: Calculating the Final Amount after Interest

Mr White deposited £5000 into a bank for 5 years, earning 2% interest on his money per year. How much will he have in his account after the 5 years?

P =P = Principal amount = £5000= £5000

R =R = Rate of interest = 2\% = 0.02= 2\% = 0.02

T =T = Time = 5= 5 years

Interest: I=\frac{P \times R \times T}{100} = \frac{£5000 \times 2 \times 5}{100} = £500I=\frac{P \times R \times T}{100} = \frac{£5000 \times 2 \times 5}{100} = £500

The interest for 5 years is £500. So, at the end of 5 years, Mr White will have £5000 (principal) + £500 (interest) = £5500 (final amount).

Example 2: Calculating Interest and Total Amount Paid for a Loan

Bernard took a loan of £10,000 from his bank and will pay interest on this sum for 10 years at the rate of 5% per annum. Find how much interest he should pay after 10 years and the total amount he paid.

P = £10,000P = £10,000

R = 5R = 5%

T = 10T = 10 years

Using I=\frac{P \times R \times T}{100} =\frac{£10,000 \times 5 \times 10}{100} = £5000I=\frac{P \times R \times T}{100} =\frac{£10,000 \times 5 \times 10}{100} = £5000

This is the interest Bernard will pay after 10 years. The total amount of money to be repaid is £10,000 (principal) + £5,000 (interest) = £15,000 (total amount paid).

Example 3: Finding the Amount Borrowed

A sum of money was borrowed from a bank at a 7.5% interest per year for 4 years. The interest amounted to £150. What is the amount borrowed?

Using I=\frac{P \times R \times T}{100}I=\frac{P \times R \times T}{100} and PP is unknown:

150 =\frac{P \times 7.5 \times 4}{100}150 =\frac{P \times 7.5 \times 4}{100}

150 =\frac{30P}{100}150 =\frac{30P}{100}

15,000=30P15,000=30P

P = 500P = 500

The amount borrowed is £500.

Example 4: Finding the Interest Rate per Annum

£50,000 was paid to Mrs Mary after investing £40,000 for 6 years into a bank. Find the interest rate per annum.

Using I=\frac{P \times R \times T}{100}I=\frac{P \times R \times T}{100} with I = £50,000 - £40,000 = £10,000I = £50,000 - £40,000 = £10,000 and T = 6T = 6 years, we have:

10,000 =\frac{40,000 \times R \times 6}{100}10,000 =\frac{40,000 \times R \times 6}{100}

10,000 =\frac{240,000R}{100}10,000 =\frac{240,000R}{100}

10,000 = 2400R10,000 = 2400R

R =\frac{10,000}{2400} = 4.166...R =\frac{10,000}{2400} = 4.166...

R = 4.2R = 4.2% (to one decimal place)

Example 5: Finding the Loan Duration

A sum of £4500 was borrowed from a firm paying 2.5% interest rate per annum. The interest paid was £750. Find how long the sum was loaned.

Using I=\frac{P \times R \times T}{100}I=\frac{P \times R \times T}{100} with I = £750I = £750, P = £4500P = £4500, and R = 2.5R = 2.5, we have:

750 =\frac{4500 \times 2.5 \times T}{100}750 =\frac{4500 \times 2.5 \times T}{100}

750 = 112.5T750 = 112.5T

T =\frac{750}{112.5}T =\frac{750}{112.5}

T = 6\frac{2}{3}T = 6\frac{2}{3} years

T = 6T = 6 years, 88 months

Example 6: Calculating Interest Earned in a Specific Time Period

£500 is deposited into a bank paying a 3% interest rate per annum. How much interest is earned in 4 months?

Using I=\frac{P \times R \times T}{100}I=\frac{P \times R \times T}{100} with P = £500P = £500, R = 3R = 3, and T=\frac{4}{12}T=\frac{4}{12} (4 months is \frac{4}{12}\frac{4}{12} of a year), gives:

I=\frac{500 \times 3 \times \frac{4}{12}}{100}I=\frac{500 \times 3 \times \frac{4}{12}}{100}

I = £5I = £5

The interest earned in 4 months is £5.

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