Question

A principal of N2500 is invested at 2% interest. Find the amount after 20 years if the interest is compounded (a) annually, (b) semi-annually, (c) quarterly, (d) monthly, and (e) daily. 

Answer 1

$A=P(1+\frac{r}{n})^{nt}$

Compounded annually n=1

$=N2500(1+\frac{0.02}{1})^{1×20}$

$= 2500(1.02)^{20} = N3714.87$

$A=P(1+\frac{r}{n})^{nt}$

Compounded semi-annually n=2

$=N2500(1+\frac{0.02}{2})^{2×20}$

$=2500(1.01)^{40} =N3722.16$

$A=P(1+\frac{r}{n})^{nt}$

Compounded quarterly n=4

$=N2500(1+\frac{0.02}{4})^{4×20}$

$= 2500(1.005)^{80} =N3725.85$

$A=P(1+\frac{r}{n})^{nt}$

compounded monthly n =12

$=N2500(1+\frac{0.02}{12})^{12×20}$

$=2500(1.001667)^{240} =N3728.62$

$A=P(1+\frac{r}{n})^{nt}$

compounded daily n=365

$=N2500(1+\frac{0.02}{365})^{365×20}$

$=2500(1.000054795)^{7300}= N3729.53$