interest and compound: A man wishes his son to receive P200,000 ten years from now

Sydney Sales's picture

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
$F = P(1 + i)^n$
 

econ_004-future-amount.gif

$F_5 = P(1 + 0.10)^5$

$F_5 = 1.10^5P$
 

$F_{10} = F_5(1 + 0.03)^{20}$

$F_{10} = 1.10^5P(1.03^{20})$

$F_{10} = (1.10^5)(1.03^{20})P$
 

$F_{10} = 20\,000$

$(1.10^5)(1.03^{20})P = 20\,000$

$P = \text{P}6,875.78$       answer

Solution 2
$P = \dfrac{F}{(1 + i)^n}$
 

econ_004-present-amount.gif

 

$P_5 = \dfrac{20\,000}{(1 + 0.03)^{20}}$

$P_5 = \text{P}11,073.52$
 

$P_0 = \dfrac{P_5}{(1 + 0.10)^5}$

$P_0 = \dfrac{11,073.52}{1.10^5}$

$P_0 = \text{P}6,875.78$
 

$P = P_0$

$P = \text{P}6,875.78$       answer