Q.A sum of ₹5,000 is invested at 8% per annum compound interest for 5 years. Using logarithms (given $\log 1.08 = 0.0334$, $\log 5 = 0.6990$, and antilog $0.8661 = 7.347$), find the compound amount and the compound interest.

The compound-amount formula contains a fifth power, which logarithms turn into a single multiplication and addition before one antilog recovers the amount.

The compound-amount formula is

Take logarithms of both sides (product and power laws):

Now $\log 5000 = \log(5\times1000) = \log 5 + 3 = 0.6990 + 3 = 3.6990$, and $5\log 1.08 = 5\times0.0334 = 0.1670$. So

Take the antilogarithm: the mantissa 0.8661 gives digits 7347, and the characteristic 3 gives 4 digits before the point: …

Cross-check by direct expansion. $(1.08)^{5} = 1.08\times1.08\times1.08\times1.08\times1.08 = 1.46933$ (to 5 d.p.). Then $A = 5000 \times 1.46933 = 7346.6 \approx ₹7{,}347$, and $\text{CI} = 7346.6 - 5000 = ₹2{,}346.6 \approx ₹2{,}347$. The direct calculation ag …

A frequent error is applying the power to the whole principal — writing $\log A = 5(\log 5000 + \log 1.08)$ — instead of only to the factor being raised to the power: the exponent 5 multiplies $\log 1.08$ alone, since only $(1.08)$ is raised to the 5th power, not …