Answer to Question #289011 in Economics of Enterprise for Daemus

Question

A man wishes to have an amount of P2,769.84 after 5 years. He deposited P500 each year into a savings bank that pay “r” percent per annum compounded continuously. Compute the value of “r”. 

Answer 1

Continuous compounding is given as;

$P(t)=P_oe^{rt}$

where

$P(t)=2769.84$

$P_o=500$

$t=5$

to find the value of r, we replace the known variables to the equation as follows;

$2769.84=500e^{5r}$

dividing by 500 on both sides of the equation;

$5.53968=e^{5r}$

equivalent to;

$e^{5r}=\frac{34623}{6250}$

we take the natural logs from both sides to eliminate e

$5rlne=ln34623-ln6250$

$r=\frac{ln34623-ln6250}{5}$

substituting the values of $ln$ and dividing by 5 we get;

$r=0.34$