Question 3
Three years ago, Brijesh purchased a buffalo from Surjeet for ₹7,680. What payment will discharge his debt now if the rate of interest is 12½% per annum, compounded annually?Solution
Given:
Principal (P) = ₹7,680
Rate (R) = \(12\frac{1}{2}%\) per annum
Time (T) = 3 years
Step 1: Write the formula
\[
A=P\left(1+\frac{R}{100}\right)^T
\]
Step 2: Substitute the values
\[
A=7680\left(1+\frac{12.5}{100}\right)^3
\]
\[
=7680\left(1+\frac{1}{8}\right)^3
\]
\[
=7680\left(\frac{9}{8}\right)^3
\]
Step 3: Calculate the amount
\[
=7680\times\frac{9}{8}\times\frac{9}{8}\times\frac{9}{8}
\]
\[
=120\times9\times9\times9
\]
\[
=120\times729
\]
\[
=₹87,480
\]
Step 4: Calculate compound interest
\[
\text{C.I.}=\text{Amount}-\text{Principal}
\]
\[
=87,480-7,680
\]
\[
=₹79,800
\]
Answer: Brijesh must pay ₹87,480 to discharge his debt now.
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