Answer to Question #306618 in Financial Math for Ndi

Question

If 35 000 accumulates to 48 328 at a continuous compounded rate of year then the term under consideration is

Answer 1

Solution

Using the Formula

$A=Pe^{rt}$

Here $A$ is the amount accumulated, $P$ is the principal amount invested, $r$ is the interest rate and $t$ is the tenure.

Therefore, we can write,

$48328=35000(e^{rt})$

$e^{rt}=\frac{48328}{35000}$

$e^{rt}=1.3808$

$ln(e^{rt})=ln(1.3808)$

$rt\times ln(e)=ln(1.3808)$

$rt\times (1)=ln(1.3808)$

$t=\frac{ln(1.3808)}{r}$

Therefore, knowing the value of $r$, we can find the tenure.

For example if $r=6.8\%$

Then

$t=\frac{ln(1.3808)}{6.8\%}$

$t=\frac{ln(1.3808)}{0.068}$

$t=4.745$  years