A person invested a certain amount of money at $10\%$ annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs $18522$ . The amount, in rupees, that the person had invested is

Entered answer:

✅ Correct Answer: 16000

A person invested money at 10% annual interest, compounded half-yearly. After 1.5 years, the total amount became Rs 18522. We need to find the original investment (principal).

When interest is compounded half-yearly:

The annual rate gets divided by 2 (since there are 2 half-years in a year)

Interest is calculated and added to the principal twice per year

So our 10% annual rate becomes 5% per half-year.

Compound Interest Formula: Amount = P(1 + r/100)ⁿ

Where:

P = Principal (what we want to find)

r = Rate per period = 5% (half-yearly rate)

n = Number of periods = 3 (since 1.5 years = 3 half-year periods)

Amount = Rs 18522

$18522 = P\left(1 + \frac{5}{100}\right)^3$

$18522 = P(1.05)^3$

Calculating $(1.05)^3$ :

$1.05^2 = 1.05 × 1.05 = 1.1025$

$1.05^3 = 1.1025 × 1.05 = 1.157625$

So: $18522 = P × 1.157625$

$P = \frac{18522}{1.157625} = 16000$

Half-yearly compounding means dividing annual rate by 2 and doubling the time periods. Always convert time to match the compounding frequency. The formula $P(1 + r/100)^n$ is essential for compound interest problems.

Answer: Rs 16000

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A person invested a certain amount of money at $10\%$ annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs $18522$ . The amount, in rupees, that the person had invested is