A certain principal invested at compound interest payable yearly amount to Rs. 10816.00 in 3 years and Rs. 11248.64 in 4 years. What is the rate of interest?
4%
To determine the rate of interest for the compounded investment, let's analyze the information given. The amount increases from Rs. 10816 in 3 years to Rs. 11248.64 in 4 years.
We will use the compound interest formula:
\(A = P(1 + r)^n\)
where \(A\) is the amount, \(P\) is the principal, \(r\) is the rate of interest per annum, and \(n\) is the number of years.
Given:
- \(A_3 = 10816\) (amount at the end of 3 years)
- \(A_4 = 11248.64\) (amount at the end of 4 years)
Let's find the rate of interest using the relationship between the amounts in consecutive years:
From the formula: \(A_4 = A_3 \times (1 + r)\)
This becomes:
\(11248.64 = 10816 \times (1 + r)\)
Simplifying for \(r\):
\(1 + r = \frac{11248.64}{10816}\)
Calculate the right-hand side:
\(1 + r = 1.04\)
Thus, \(r = 1.04 - 1 = 0.04\), which is equal to \(4\%\).
Hence, the rate of interest is 4%.
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