Question

Find the compound interest on #650 in 5years at 4% per annum

Answer 1

To calculate the compound interest on an amount using the formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (initial investment).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of times that interest is compounded per year.
- \(t\) is the number of years the money is invested or borrowed for.

In this instance:
- \(P = 650\)
- \(r = 0.04\) (4% as a decimal)
- \(n = 1\) (assuming interest is compounded annually)
- \(t = 5\)

Substituting the values into the formula:

\[
A = 650 \left(1 + \frac{0.04}{1}\right)^{1 \cdot 5}
\]
\[
A = 650 \left(1 + 0.04\right)^{5}
\]
\[
A = 650 \left(1.04\right)^{5}
\]

Calculating \( (1.04)^5 \):
\[
(1.04)^5 \approx 1.216652902
\]

Now, substituting this back into the calculation for \(A\):
\[
A \approx 650 \times 1.216652902 \approx 790.83
\]

Now, to find the compound interest:
\[
\text{Compound Interest} = A - P
\]
\[
\text{Compound Interest} \approx 790.83 - 650 \approx 140.83
\]

Thus, the compound interest on ₹650 in 5 years at 4% per annum is approximately **₹140.83**.