Answer to Question #211548 in Quantitative Methods for Girl

Question

find the number of years it would take for 748 to increase by 72 percent if invested at interest rate 7.9 percent per annum, compounded semi-annually

Answer 1

Given,

Principal amount = 748

Increased amount = 72 % of 748

So, total amount = $\frac{172\times 748 }{100} =1286.56$

Rate of interest = 7.9% per annum compounded semi annually

So, rate of interest for the semi annual $= \frac{7.9}{2} = 3.45$ %

$A= P(1+R\%)^n$

$\Rightarrow 1286.56 = 748(1+\frac{3.45}{100})^n$

$\Rightarrow 1.72=1.0345^n$

Taking log of both side,

$\Rightarrow n= \frac{\log(1.72)}{\log(1.0345)}$

$\Rightarrow n = 15.98$

$\Rightarrow n \simeq 16$

Hence, total number of year will be 8 years.