5.3 Interest rate compounding

Interest rate compounding is an extremely important concept. The basic idea is that when you save money in a savings account, then you earn interest on:

  1. The money you originally deposited.

    And

  2. The interest that you earn.

Have a go at the examples in the following activities to understand the power of compounding.

Quiz 1 – The power of compounding

Timing: Allow 5 minutes

a. 

£556.20


b. 

£560.00


c. 

£561.80


The correct answer is c.

Answer

This example is slightly more complicated than the example in which Sarah deposited her savings of £500 for 1 year. In the present case, you can think about Sarah’s savings growing in two steps.

Step 1 – Savings after 1 year:

After the first year, Sarah will have £530. This is calculated as in the earlier example. Specifically, the amount after 1 year is calculated as:

500 × 1.06 = £530

After 1 year, Sarah has earned £30 of interest.

Step 2 – Savings after 2 years:

In the second year, Sarah will earn interest of 6% on her original savings of £500. In addition, she will earn interest on the interest she earned in the first year.

So, in the second year, she will earn:

  1. interest on £500, which is equal to £500 × 0.06 = £30

  2. interest on £30, which is equal to £30 × 0.06 = £1.80

After 2 years, Sarah will have in her account:

  1. the original £500 that she deposited in the savings account.

  2. £30 interest earned during the first year on the original £500.

  3. £30 interest earned during the second year on the original £500.

  4. £1.80 interest earned during the second year on the £30 interest from year 1.

The total amount in Sarah’s savings account will be:

500 + 30 + 30 + 1.80 = £561.80

Instead of doing the complicated computation above, you can compute the payment after 2 years as follows:

500 × (1.06)2 = £561.80

Computing payment with interest rate compounding

You can use the following formula to compute payment with interest rate compounding.

Suppose you deposit £X for N years in a savings account. The interest rate on the savings account is R% compounded annually.

The amount in your savings account after N years will be:

X × (1.0R)N

The following video explains the above formula with examples.

Interactive feature not available in single page view (see it in standard view).

Quiz 2 – The power of compounding

Timing: Allow 5 minutes

a. 

£64,326.12


b. 

£72,430.16


c. 

£89,850.08


The correct answer is c.

Answer

We can use the same approach that we followed to compute interest payment for two years in the previous example.

The key differences between this and the earlier example are:

  1. the initial deposit is now £10,000 and not £500.

  2. the interest rate is now 5% and not 6%.

  3. the time period is now 45 years and not 2 years.

So, the amount that Ash will have in her savings account is:

£10,000 × (1.05)45 = £89,850.08

This example shows you how money grows in the form of long-term savings due to the power of compound interest.

5.2 Interest rates

5.4 Inflation, again!