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Interest

Interest is the fee that a borrower pays to a lender for the use of the borrowed money. In other words, when money is borrowed, the lender expects to be paid back the amount of the loan plus an additional money for the use of the money, that additional money is called interest. Similarly when money deposited in a bank, the depositor is paid for the use of the money. The deposit earns is also called interest.

Interest is calculated in two ways:

• Compound interest

• Simple interest

Interest Formula

Simple interest:It is the amount paid on the original principal amount. The formula to calculate simple interest is given below:

Simple interest formula

S.I = $\frac{P \times R \times T}{100}$

Where I is the interest, P is the principal, r is the interest rate and t is the time period.
Compound interest: Unlike simple interest, compound interest is the interest paid on the principal plus the accumulated interest. In compound interest, the interest is applied a number of times during the term of an investment. The formula is used for any type of compounding, annually, semiannually, monthly, weekly and so on.

Compound Interest Formula

CI = A - P

A = P (1 + $\frac{R}{n}$)$^{nT}$

Where:
CI = Compound interest
A = Compound amount
P = Principal amount
R = Annually interest rate
t   = Number of years
n = Number of times the interest is compounded per year

Solved Examples on Interest

Example 1:
Calculate the simple interest earned in 1 year on a deposit of $\$$500 if the interest rate is 3%. Solution: Formula for simple interest is S.I = \frac{P \times R \times T}{100} where, S.I =Simple Interest P = Principal = 500 R = Interest rate = 3 T = Time Period = 1 To find simple interest plug in the given values in the formula, we get S.I = \frac{500 \times 3 \times 1}{100} = 15 The simple interest earned is \$$ 15. Example 2: Richal deposits$\$$1500 for 1 years at 2% interest, compounded daily. What is his ending balance? Solution: Given: P = 1500, t = 1, n = 365 and R = 2% Use the compound interest formula CI = P (1 + \frac{R}{n})^{nT} = 1500 (1 + \frac{2}{100 \times 365})^{365 \times 1} = 1500 (6.48)^{1460} = 1500 \times 1.68 = 2520 Richal's ending balance is \$$ 2520.

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