Question

(1) Sampatrao took a loan of Rs 25,000 to pay medical bills. He returned the loan by paying Rs 28,500 after two years. What was the rate of interest?

(2) Find the interest on Rs 7,500 at the rate of 13% per annum after $3\frac{1}{2}\mathrm{years}$.

Answer 1

(1) Amount (A) = Rs 28,500
Principal (P) = Rs 25,000
Time (N) = 2 years
Interest (I) = Amount – Principle
= Rs 28,500 – Rs 25,000
= Rs 3,500

$$\begin{gathered} \mathrm{I}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{N}}{100} \\ \text{or}3500=\frac{25000\times \mathrm{R}\times 2}{100} \\ \text{or}3500=250\times \mathrm{R}\times 2 \end{gathered}$$

or 3500 = 500 × R
or $\frac{3500}{500}=\mathrm{R}$ (On dividing both sides by 500)
or R = 7%
∴ Rate of interest is 7%

(2) Principal (P) = Rs 7,500
Time (N) = $3\frac{1}{2}=\frac{7}{2}$ years
Rate (R) = 13%
Interest ( I ) = ?
We know,
$$\begin{gathered} \mathrm{I}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{N}}{100} \\ \mathrm{I}=\frac{7500\times 13\times {\displaystyle \frac{7}{2}}}{100} \\ \mathrm{I}=\frac{3750\times 13\times 7}{100} \\ \mathrm{I}=\frac{375\times 13\times 7}{10} \\ \mathrm{I}=\frac{75\times 13\times 7}{2} \\ \mathrm{I}=\mathrm{Rs}3412.50 \end{gathered}$$