Question

5.) A man deposits P500 at the end of each year and expected to have an amount of P2,769.84 at the end of 5 years.

1. What is the nominal rate of interest if it is compounded annually?

2. What is the nominal rate of interest if it is compounded continuously?

3. Compute the equivalent compound amount factor if it is compounded continuously

Ans. 1. 5.127% 2. 5% 3. 5.3968

Answer 1

$2769.84=500(1+\frac{r}{100})^5$

$5.54=(1+\frac{r}{100})^5$

$1.41=(1+\frac{r}{100})$

r=$5.127\%$

$P(t)=P(o)e^{rt}$

$2769.84=500\times e^{5r}$

$5.54=$ $e^{5r}$

$r=5\%$

$compounding factor= e^{rt}$

$r=5, t=5$

$e^{25} =5.3968\%$