# Compound Interest-10th Grade-1

### From Homeworkwiki

**Mr. Bill is paid at the rate of 5% per annum compound interest payable half-yearly. What rate of interest per annum does he get?**

**Solution:** Let the principal (P) = $100

Here, rate of interest (r %) = 5%

Time (n) = 1 year = 2 half years

So, amount after 1 year = $100 * (1 + 5/100)^{2}

= $100 * (1 + 1/40)^{2}

= $100(41/40)^{2}

= $100 * 41/40 * 41/40

=$105.0625

So, the compound interest in 1 year = $(105.0625 – 100)

= $5.0625

So, the Mr. Bill actually receives $5.0625 as interest on $100 in 1 year

So, the required rate of interest per annum is 5.0625%.