# Compound Interest

Compound interest arises when interest is added to the principal , so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding .
Note: The main difference between simple interest and compound-interest is that in case of simple interest, the principal remains the same throughout, whereas in the case of compound-interest, it goes on changing periodically.

Example :

1)A bank account, for an account with \$1000 initial principal and 20% interest per year would have

Solution :
I = P x r x t

I = 1000 x 0.2 x 1

I = \$200

A = P + I

A= \$1200 at the end of 1st year.

I = P x r x t

I = 1200 x 0.2 x 1

I = 240

A = P + I

A= \$1440 at the end of 2nd year and so on.

Here we have counted interest on interest, but this is a bit longer method. So we will use a formula to calculate directly the amount say after 3 yrs., 4 yrs. and so on.
 A = P ( 1 + r )t

Where P = Principal
r = rate in percent
t = time period in years.

I = Interest = A – P

Example :

1) Find the compound-interest in \$8000 for 2 years at 6% p.a.

Solution :
Principal = P = \$8000, Rate = r = 6% = 6/100 = 0.06 and
time period = t = 2 years
 A = P ( 1 + r )t A = 8000 ( 1 + 0.06)2 A = 8000 (1.06)2 A = 8000 x 1.1236 A = \$8988.8 I = A - P I = 8988.8- 8000 I = \$988.80

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2) Find the compound interest on \$24,000 at 15% p.a for 2
years.

Solution :
P = \$24,000, R = 15% and Time = t = 2

When time is in fraction then amount is given by the following formula.

Amount after 2 years = P ( 1 + r )2(1 + r/3)

= 24000( 1 + 0.15)
2 ( 1 + 0.15/3)

= 24000 x (1.15)
2 x ( 1 + 0.05)

= 24000 x 1.3225 x 1.05

Amount = \$ 33,327

∴ C.I = Amount - P

= 33,327 - 24,000

C.I = \$ 9,327.

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Compound Interest (CI)

Find Compound- Interest when interest is compounded Half yearly
Find Compound- Interest when interest is compounded Quarterly
Find CI when interest is compounded annually but Rates are different
Finding Principal
Finding Time Period of Investment
Finding Rate of Interest