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### Formulas of Problems on Compound Interest - Aptitude Questions and Answers.

TIPS FOR SOLVING QUESTIONS RELATED TO COMPOUND INTEREST:

Compound Interest: The money is said to be lent on compound interest (C.I.) if the interest at the end of a year or some specified period is not paid to the lender, but is added to the principal, so that the amount at the end of this period becomes the principal for the next period. This process is repeated until the amount for the last period is obtained.
After the specified period, the difference between the amount and the money borrowed (principal) is called the compound interest (C.I.)

Compound Interest (C.I.) = Amount (A) - Principal (P)

1. If Principal = P, Rate = R% per annum, Amount = A, Time = n years, then
Compound Interest Formula when interest is compounded Annually:

\begin{aligned}
Amount (A) = P\left( 1 + \frac{R}{100} \right)^n \\
\end{aligned}

2. Compound Interest Formula when interest is compounded Half Yearly :
\begin{aligned}
Amount (A) = P\left( 1 + \frac{R/2}{100} \right)^{2n} \\
\end{aligned}

Tips: If the interest is payable half yearly, then time is multiplied by 2 and rate is divided by 2.

3. Compound Interest Formula when interest is compounded Quarterly:

\begin{aligned}
Amount (A) = P\left( 1 + \frac{R/4}{100} \right)^{4n} \\
\end{aligned}

Tips: If the interest is payable quarterly, then time is multiplied by 4 and rate is divided by 4.

4. When interest is compounded Annually but time is in fraction, for e.g. \begin{aligned}2\frac{3}{5} years \end{aligned}
then Amount will be,

\begin{aligned}
Amount (A) = P\left( 1 + \frac{R}{100} \right)^2 \times \left( 1 + \frac{\frac{3}{5}R}{100} \right)
\end{aligned}

5. When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.

Then Amount will be,
\begin{aligned}
Amount (A) = P\left( 1+\frac{R1}{100} \right) \left( 1+\frac{R2}{100} \right) \left( 1+\frac{R3}{100} \right)
\end{aligned}

6. Present worth of Rs. x due n years hence will be:

\begin{aligned}
\text{Present Worth} = \frac{x}{\left(1+\frac{R}{100}\right)^n}
\end{aligned}