Everything Maths Grade 10

The amountA 1 becomes the new principal amount for calculating the accumulated amount at the end of the
second year.

A 2 =P(1 +i)

= 1050 (1 +0,05)

= 1000 (1 +0,05) (1 +0,05)

= 1000 (1 +0,05)^2

Similarly, we use the amountA 2 as the new principal amount for calculating the accumulated amount at the
end of the third year.

A 3 =P(1 +i)

= 1000 (1 +0,05)^2 (1 +0,05)

= 1000 (1 +0,05)^3

Do you see a pattern?

Using the formula for simple interest, we can develop a similar formula for compound interest.

With an opening balancePand an interest rate ofi, the closing balanced at the end of the first year is:

Closing balance after 1 year=P(1 +i)

This is the same as simple interest because it only covers a single year. This closing balance becomes the
opening balance for the second year of investment.

Closing balance after 2 years= [P(1 +i)](1 +i)

=P(1 +i)^2

And similarly, for the third year

Closing balance after 3 years=

[

P(1 +i)^2

]

(1 +i)

=P(1 +i)^3

We see that the power of the term(1 +i)is the same as the number of years. Therefore the general formula
for calculating compound interest is:

A=P(1 +i)n

Where:

A= accumulated amount

P= principal amount

i= interest written as a decimal

n= number of years

336 9.3. Compound interest