A man wishes his son to receive P200 000 ten years from now. What amount should he invest now if it will earn interest of 10% compounded annually during the first 5 years and 12% compounded quarterly during the next 5 years.
A man wishes his son to receive P200 000 ten years from now. What amount should he invest now if it will earn interest of 10% compounded annually during the first 5 years and 12% compounded quarterly during the next 5 years.
Solution 1
$F = P(1 + i)^n$
$F_5 = P(1 + 0.10)^5$
$F_5 = 1.10^5P$
$F_{10} = F_5(1 + 0.03)^{20}$
$F_{10} = 1.10^5P(1.03^{20})$
$F_{10} = (1.10^5)(1.03^{20})P$
$F_{10} = 20\,000$
$(1.10^5)(1.03^{20})P = 20\,000$
$P = \text{P}6,875.78$ answer
Wrong answer. The future worth is 200,000 not 20,000
F = 200,000. Therfore P=68757.81
Solution 2
$P = \dfrac{F}{(1 + i)^n}$
$P_5 = \dfrac{20\,000}{(1 + 0.03)^{20}}$
$P_5 = \text{P}11,073.52$
$P_0 = \dfrac{P_5}{(1 + 0.10)^5}$
$P_0 = \dfrac{11,073.52}{1.10^5}$
$P_0 = \text{P}6,875.78$
$P = P_0$
$P = \text{P}6,875.78$ answer
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