Solution 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.
Home » Aptitude » Compound Interest » Question
Since Interest accumulates half yearly so effective rate = R/2 = 4/2 = 2.And effective time is 2t. ∵ 6250 [1 + 2/100]2t = 6632.55 ⇒ (1 +2/100)2t = 663255/625000 = 132651/125000 = (51/50)3 ⇒ (51/50)2t = (51/50)3⇒ 2t =3 ∴ t = 3/2 years
|