A sum of money,deposited at some rate p.c.p.a | vedclass

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(A) Let the principal amount be $P$ and the rate of interest be $r$ per annum. The formula for compound interest is $A = P(1 + \frac{r}{100})^n$,where

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$16$

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(A) Let the principal amount be $P$ and the rate of interest be $r$ per annum. The formula for compound interest is $A = P(1 + \frac{r}{100})^n$,where $n$ is the time in years.According to the problem,the sum doubles in $4$ years:$2P = P(1 + \frac{r}{100})^4$$2 = (1 + \frac{r}{100})^4$  --- (Equation $1$)We want to find the time $t$ in which the sum becomes $16$ times itself:$16P = P(1 + \frac{r}{100})^t$$16 = (1 + \frac{r}{100})^t$Since $16 = 2^4$,we can write:$2^4 = (1 + \frac{r}{100})^t$Substitute the value of $2$ from Equation $1$:$((1 + \frac{r}{100})^4)^4 = (1 + \frac{r}{100})^t$$(1 + \frac{r}{100})^{16} = (1 + \frac{r}{100})^t$Comparing the exponents,we get $t = 16$ years.

$A$ sum of money,deposited at some rate $p.c.p.a.$ of compound interest,doubles itself in $4$ years. In how many years will it become $16$ times of itself at the same rate?

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