Answer to Question #182055 in Macroeconomics for SYEDA ZAINAB

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 interest

at the end of each year, what would be his yearly earnings from the investment if added (i) yearly, (ii) six-monthly, (iii) quarterly, (iv) monthly, and (v) continuously?

Answer 1

1)we will find it by the formula,

interest rates are divided into the number of periods

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

(i) yearly

$FV=100 000(1+0.18)^5=228775.78$

(ii) six-monthly

$FV=100 000(1+\frac{0.18}{2})^{10}=236736.37$

(iii) quarterly

$FV=100 000(1+\frac{0.18}{4})^{20}=241 171.40$

(iv) monthly

$FV=100 000(1+\frac{0.18}{12})^{60}=244321.98$

(v) continuously.

$FV=PV*e^{qn}=100 000\times2.71828^{0.18\times5}=245960.16$

2)we will find it by the formula, interest rates are divided into the number of periods

 (i) yearly

$FV=100 000\frac{(1+0.18)^5-1}{0.18}=715420.98$

(ii) six-monthly

$FV=100 000\frac{(1+0.09)^{10}-1}{0.09}=1 519 292.97$

(iii) quarterly

$FV=100 000\frac{(1+0.045)^{20}-1}{0.045}=3 137 142.27$

(iv) monthly,

$FV=100 000\frac{(1+0.015)^{60}-1}{0.015}=9 621 465.2$

and (v) continuously

$FV=\frac{PV}{r}=\frac{100 000}{0.18}=555 555.56$