In what time will Rs. 6,250 amount to Rs. 6,632.55 at 4% compound interest payable half-yearly?

If the principle amount 'P' when compounded half-yearly at R% interest rate per annum for 'n' years, the new amount is P'.

then $$P' = P{[1 + \frac{R}{2\times 100}]}^{n}$$

Given P' = 6,632.55, P = 6,250 and R = 4%

$$\Rightarrow 6,632.55 = 6,250{[1 + \frac{4}{2\times 100}]}^{n}$$

$$\Rightarrow 1.061 = {1.02}^{n}$$

Taking logarithm on both sides we get,

n = log(1.061)$$\div$$log(1.02) = 3

Since n refers to half a year in this case, the number of years will be $$\frac{3}{2}$$ years.