Question

Q:1 An investor deposits a sum of Rs 100,000 in an investment company with a promise of a rate of return of 18 percent per year. What will the sum amount be at the end of 5 years if the interest is added (i) yearly,(ii) six-monthly, (iii) quarterly, (iv) monthly, and (v) continuously.

• From the information given in Question #1, if the investor decides to withdraw the accumulated interestat the end of each year, what would be his yearly earnings from the investment if added (i) yearly, (ii) sixmonthly,(iii) quarterly, (iv) monthly, and (v) continuously?

Answer 1

The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

$FV = PV(1 + \frac{r}{m})^{mt}$

or $FV=PV(1+i)^n$

Onemay solve for the present value PV to obtain:

$PV=\frac{FV}{1+\frac{r}{m}}^{mt}$

where $i=\frac{r}{m}$ is the interest per compounding period and $n=mt$ is the number of compounding periods.

(i) Yearly

$PV=\frac{FV}{1+\frac{r}{m}}^{mt}$

$FV = PV(1 + \frac{r}{m})^{mt}$

$=100,000(1+\frac{0.18}{12})^5$

$=Rs 107,728.40$

(ii) sixmonthly

$PV=\frac{FV}{1+\frac{r}{m}}^{mt}$

$FV = PV(1 + \frac{r}{m})^{mt}$

$=100,000(1+\frac{0.18}{2})^{5\times2}$

$=Rs 236,736.37$

(iii) quarterly

$PV=\frac{FV}{1+\frac{r}{m}}^{mt}$

$FV = PV(1 + \frac{r}{m})^{mt}$

$=100,000(1+\frac{0.18}{4})^{4\times5}$

$=Rs 241,171.40$

(iv) monthly

$PV=\frac{FV}{1+\frac{r}{m}}^{mt}$

$FV = PV(1 + \frac{r}{m})^{mt}$

$=100,000(1+\frac{0.18}{12})^{12\times5}$

$=Rs 244,321.98$

(v) continuously

$PV=\frac{FV}{1+\frac{r}{m}}^{mt}$

$FV=PV(1+i)^n$

$=100,000(1+0.18)^{5}$

$=Rs 228,775.78$