Compound Interest Formula
The compound interest formula is widely used for calculating interest. When using the compound interest, for the first period it is similar to the simple interest. The difference occurs in and from the second period of time. From the second period, the interest is also calculated on the interest thus earned on the previous period of time, that is why it is known as interest on interest. In this section, we will be discussing the various aspects of the compound interest formula, and understand the variables involved.
What is the Compound Interest Formula?
The compound interest formula is widely used for calculating interest. When using the compound interest, for the first period it is similar to the simple interest. The difference occurs in and from the second period of time.
Compound Interest Formula = P(1 + (r/n) )^{nt } P
Where,
 P is the principal amount
 r is the interest rate in decimal form
 t is the time
 n represents the number of times interest is compounded per unit time.

Example 1: Sam lends $1,500 to his friend at an annual interest rate of 4.3%, compounded quarterly. Using the compound interest formula calculate what will be the interest after 6 years?
Solution:
To find: Compound interest accumulated after 6 years.
P = 1500, r = 0.043 (4.3%), n = 4, and t = 6 (given)
Using compound interest formula,
CI = P(1 + (r/n) )^{nt } P
Put the values,
CI = 1500(1 + (0.043/4))^{4*6} 1500
CI = 1938.84  1500
CI = 438.84
Answer: The compound interest after 6 years will be $438.84.

Example 2: James borrowed $600 from the bank at some rate compounded halfyearly and that amount becomes quadruple in 4 years. Calculate the rate at which James borrowed the money.
Solution:
To find: Interest rate
P = 600, n = 2, and t = 4, Amount = 2400 (given)
Using formula,
CI = Amount  Principal
Put the values,
CI = 2400  600 = 1800
Using compound interest formula,
CI = P(1 + (r/n) )^{nt } P
Put the values,
1800 = 600(1+ (r/2))^{2*4 } 600
2400 = 600(1+ (r/2))^{8}
4 = (1+ (r/2))^{8}
1 + (r/2) = 1.189
r/2 = 0.189
r = 0.378
Answer: The interest rate on the given amount of money is 37.8%.