Compound Interest Practice Questions with Detailed Solutions – Level 3

Compound Interest Level 3 Practice Questions on CI, Instalments and Growth

Compound Interest Level 3 is an advanced arithmetic practice set on compound interest. It covers half-yearly and quarterly compounding, CI and SI differences, equal instalments, and population and depreciation changes. Aptitude360 includes a worked solution for every question. The set suits learners who already know the basic amount formula and want harder, multi-step problems.

Topics covered in this Compound Interest Level 3 set

• Interest for fractional periods with half-yearly and quarterly compounding
• Finding the principal or rate from a given compound interest
• Difference between compound and simple interest over two and three years
• Loans repaid in equal annual instalments, and unequal instalments
• Different rates in successive years
• Population growth with birth and death rates, and depreciation of machines and cars
• Time taken for a sum to become a multiple of itself

Key compound interest formulas for Level 3

• Amount, compounded annually: \( A=P\left(1+\dfrac{R}{100}\right)^{n} \)
• Compounded half-yearly, n years: \( A=P\left(1+\dfrac{R}{200}\right)^{2n} \)
• CI minus SI, two years (annual compounding, constant rate): \( P\left(\dfrac{R}{100}\right)^{2} \)
• CI minus SI, three years (annual compounding, constant rate): \( P\left(\dfrac{R}{100}\right)^{2}\left(3+\dfrac{R}{100}\right) \)
• Depreciation at a constant annual rate: \( V=P\left(1-\dfrac{R}{100}\right)^{n} \)
• Rate from interest of consecutive years (same rate each year): \( R=\dfrac{I_{2}-I_{1}}{I_{1}}\times 100 \)

Revision tips for harder compound interest problems

• Convert the annual rate into the rate per period and the time into the number of periods before applying the formula.
• For instalments, discount each payment back to the start and set the sum equal to the loan.
• Treat population and depreciation questions as successive percentage changes, multiplying one factor per year.
• For 'becomes k times' questions, remember that the growth factor raised to the time gives the multiple, so compare powers.

Who should take this set

Students preparing quantitative aptitude for competitive exams who have finished the basic compound interest levels and want hard, exam-style practice.