Find the compound interest on p7 000 at 21 per annum for 2 years 4 months compounded annually

The sooner you start to save, the more you'll earn with compound interest.

How compound interest works

Compound interest is the interest you get on:

• the money you initially deposited, called the principal
• the interest you've already earned

For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest.

This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest.

Save more with compound interest

The power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later.

For example, if you put $10,000 into a savings account with 3% interest compounded monthly:

• After five years, you'd have $11,616. You'd earn $1,616 in interest.
• After 10 years you'd have $13,494. You'd earn $3,494 in interest.
• After 20 years you'd have $18,208. You'd earn $8,208 in interest.

Compound interest formula

To calculate compound interest, use the formula:

A = P x (1 + r)n

A = ending balance
P = starting balance (or principal)
r = interest rate per period as a decimal (for example, 2% becomes 0.02)
n = the number of time periods

How to calculate compound interest

To calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly:

1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042

2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24

3. Use the compound interest formula

A = $2,000 x (1+ 0.0042)24
A = $2,000 x 1.106
A = $2,211.64

Lorenzo and Sophia compare the compounding effect

Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term.

After five years:

• Sophia has $12,834.
• Lorenzo has $12,500.

Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest.

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Imagine you put $ 100 in a savings account with a yearly interest rate of 6 % .

After one year, you have 100 + 6 = $ 106 . After two years, if the interest is simple , you will have 106 + 6 = $ 112 (adding 6 % of the original principal amount each year.) But if it is compound interest , then in the second year you will earn 6 % of the new amount:

1.06 × $ 106 = $ 112.36

Yearly Compound Interest Formula

If you put P dollars in a savings account with an annual interest rate r , and the interest is compounded yearly, then the amount A you have after t years is given by the formula:

A = P ( 1 + r ) t

Example:

Suppose you invest $ 4000 at 7 % interest, compounded yearly. Find the amount you have after 5 years.

Here, P = 4000 , r = 0.07 , and t = 5 . Substituting the values in the formula, we get:

A = 4000 ( 1 + 0.07 ) 5 ≈ 4000 ( 1.40255 ) = 5610.2

Therefore, the amount after 5 years would be about $ 5610.20 .

General Compound Interest Formula

If interest is compounded more frequently than once a year, you get an even better deal. In this case you have to divide the interest rate by the number of periods of compounding.

If you invest P dollars at an annual interest rate r , compounded n times a year, then the amount A you have after t years is given by the formula:

A = P ( 1 + r n ) n t

Example:

Suppose you invest $ 1000 at 9 % interest, compounded monthly. Find the amount you have after 18 months.

Here P = 1000 , r = 0.09 , n = 12 , and t = 1.5 (since 18 months = one and a half years).

Substituting the values, we get:

A = 1000 ( 1 + 0.09 12 ) 12 ( 1.5 ) ≈ 1000 ( 1.143960 ) = 1143.960

Rounding to the nearest cent, you have $ 1143.96 .

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