Compound interest is a type of interest that is calculated on both the principal amount and the accumulated interest of a loan or investment. The formula for calculating compound interest is:
Compound Interest = P (1 + (R / N))^(N x T) - P
Where:
P = principal amount (the amount of money borrowed or invested)
R = annual interest rate (expressed as a decimal)
N = number of times the interest is compounded per year
T = time period (in years)
Using this formula, you can calculate any of the following variables given the other three:
P = C / (1 + (R / N))^(N x T)
R = N[(C / P)^(1 / (N x T)) - 1]
N = log[(C / P) / (1 + R / N)] / (T x log(2))
Where C is the final amount including principal and interest, and log is the natural logarithm.
Here are some examples of how to use the compound interest formula:
Example 1:
Suppose you invest ₹5,000 at a compound interest rate of 6% per annum, compounded monthly, for 5 years. What will be the total amount you will receive at the end of the investment period?
Solution
Compound Interest = P (1 + (R / N))^(N x T) - P
Compound Interest = 5,000 (1 + (0.06 / 12))^(12 x 5) - 5,000
Compound Interest = ₹6,771.32
Therefore, the total amount you will receive at the end of the investment period is ₹6,771.32.
Example 2:
Suppose you borrow ₹10,000 at a compound interest rate of 8% per annum, compounded quarterly, for 3 years. What will be the total amount you will have to repay at the end of the loan period?
Solution
Compound Interest = P (1 + (R / N))^(N x T) - P
Compound Interest = 10,000 (1 + (0.08 / 4))^(4 x 3) - 10,000
Compound Interest = ₹12,597.73
Therefore, the total amount you will have to repay at the end of the loan period is ₹12,597.73.
Example 3:
Suppose you want to invest ₹3,000 at a compound interest rate of 5% per annum, compounded semi-annually, to reach a target amount of ₹5,000 in 4 years. What will be the interest rate you need to achieve your target?
Solution
Compound Interest = P (1 + (R / N))^(N x T) - P
5,000 = 3,000 (1 + (R / 2))^(2 x 4) - 3,000
2.5 = (1 + (R / 2))^(8)
log(2.5) = 8 log(1 + (R / 2))
log(2.5) / 8 = log(1 + (R / 2))
1.05 = 1 + (R / 2)
R = 0.1 = 10%
Therefore, you need an interest rate of 10% per annum, compounded semi-annually, to reach your target of ₹5,000 in 4 years.
