Compound Interest Practice Test Set 1

Total time = 1.25 years = 15 months. At 5-monthly compounding, the number of periods is 15/5 = 3.

Rate per 5-month period = 8% $\times 5/12 = 10/3%$. The growth factor is 1 + 1/30 = 31/30.

Amount = 8,100 $\times (31/30)³ =$ ₹8,937.30 .

For 2 years with annual compounding, the difference between CI and SI is P $\times (R/100)²$.

Substitute $P = 54,000$ and difference = 1,215: 1,215 = 54,000 $\times (R/100)²$.

(R/100)² = 1,215/54,000 = 9/400. Taking the positive square root, R/100 = 3/20 = 0.15.

For 2 years, CI - SI = P $\times (R/100)²$.

Substitute the values: 2,401 = 10,00,000 $\times (R/100)²$.

(R/100)² = 2,401/10,00,000 = 0.002401 = 0.049².

For 2 years, the difference between compound interest and simple interest is P $\times (R/100)²$.

405 = 18,000 $\times (R/100)²$, so (R/100)² = 405/18,000 = 9/400.

Taking the positive square root gives R/100 = 3/20 = 0.15.

Interest earned during the 2nd year is calculated on the amount at the beginning of year 2. That amount is P $\times 1.15$.

$Second-year interest = P \times 1.15 \times 0.15 = 0.1725P.$