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 |
_________________________________________________________________
2) Find the compound interest on $24,000 at 15% p.a for 2 ⅓ years.
Solution :
P = $24,000, R = 15% and Time = t = 2 ⅓
When time is in fraction then amount is given by the following formula.
Amount after 2 ⅓ 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
