Interest is the extra amount paid for borrowing money or earned by investing it. Aptitude questions commonly cover simple interest, compound interest, changing rates, depreciation, and installments.

Key terms

• Principal (P): the original sum borrowed or invested.
• Rate (R): the interest rate, usually per annum.
• Time (T): the period for which money is borrowed or invested.
• Interest (I): the additional amount earned or paid.
• Amount (A): principal plus interest.

Simple interest

In simple interest, interest is calculated only on the original principal for the entire period.

• Simple Interest = (P x R x T) / 100
• Amount = P + Simple Interest
• When time is given in months, convert it to years before applying an annual rate.

Compound interest

In compound interest, each period's interest is added to the principal. The next period's interest is then calculated on this new amount.

• Amount = P x (1 + R/100)^T for annual compounding.
• Compound Interest = Amount - Principal
• For two years, CI - SI = P x (R/100)^2.
• Use successive multipliers when the rate changes each year.

Different compounding periods

• Half-yearly: divide the annual rate by 2 and double the number of years.
• Quarterly: divide the annual rate by 4 and multiply the number of years by 4.
• For a fractional final year with annual compounding, calculate compound interest for full years and simple interest for the remaining fraction on the accumulated amount.

Depreciation and growth

• For an annual growth rate r%, multiply the value by (1 + r/100) each year.
• For annual depreciation r%, multiply the value by (1 - r/100) each year.
• Population growth, inflation, and asset value changes use the same compound-growth principle.

Installments

When payments are made at different times, calculate interest only for the time each unpaid balance remains outstanding. Treat each installment as reducing the principal on its payment date.

How to solve questions

1. Identify the principal, rate, time, and whether interest is simple or compound.
2. Make rate and time periods consistent.
3. Use the appropriate amount formula, then subtract principal if only interest is asked.
4. For different annual rates, multiply the relevant yearly factors.
5. Check whether the answer asks for interest, amount, rate, time, or principal.