# Compound Interest

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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

_________________________________________________________________
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.

_________________________________________________________________
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