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 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.
