Question

Angeline wishes to make six annual deposits in the amounts of $1,000, $2,000, $3,000,
$4,000, $5,000 and $6,000, in that order, into a fund that pays interest at rate of 5% per
annum. Determine the value of amount today if
i) the interest is compounded annually
ii) the interest is compounded quarterly.

Answer 1

solution

Part i)

Compounding per annum

Rate $r=0.05$

Present value $PV = \sum p_i(1+r)^{-i}$

$$= \frac{1000}{(1.05)^1} + \frac{2000}{(1.05)^2} + \frac{3000}{(1.05)^3}$$ $$+ \frac{4000}{(1.05)^4} + \frac{5000}{(1.05)^5} + \frac{6000}{(1.05)^6}$$

$= 17044.74$

answer: the present value is $ 17,044.74

Part ii)

Compounding quarterly

$PV = \sum p_i(1+\frac{r}{4})^{-i*4}$

$$= \frac{1000}{(1.0125)^4} + \frac{2000}{(1.0125)^8} + \frac{3000}{(1.0125)^{12}}$$ $$+ \frac{4000}{(1.0125)^{16}} + \frac{5000}{(1.0125)^{20}} + \frac{6000}{(1.0125)^{24}}$$

$=26116.03$

answer: the present value is $ 26,116.03