#### If ₹ 40000 amounts to ₹ 48620.25 in 2 years, compound interest payable half-yearly, find the rate of interest per annum.

**Solution:**

It is given that

Principal (P) = ₹ 40000

Amount (A) = ₹ 48620.25

Period (n) = 2 years = 4 half years

Consider rate of interest = r% p.a. = r/2% half yearly

We know that

A/P = (1 + r/100)^{n}

Substituting the values

48620.25/40000 = (1 + r/200)^{4}

By further calculation

(1 + r/200)^{4} = 4862025/ (100 × 40000) = 194481/160000

So we get

(1 + r/200)^{4} = (21/20)^{4}

It can be written as

1 + r/200 = 21/20

r/200 = 21/20 – 1 = 1/20

By cross multiplication

r = 200 × 1/20 = 10

Hence the rate of interest per annum is 10%.

**More Solutions:**

- Compound interest on ₹ 8000 at 5% per annum for 2 years.
- A man invests ₹ 46875 at 4% per annum compound interest for 3 years.
- Compound interest for the second year on ₹ 8000 for three years at 10% p.a.
- Ramesh invests ₹ 12800 for three years.
- Sum of money for 2 years at 12% per annum is ₹ 1380.
- At the end of one year this sum amounts to ₹ 11200.
- At the end of first year it amounts to ₹ 5325.
- At the end of one year it amounts to ₹ 5600.
- Find the amount and the compound interest on ₹ 2000.