I'm trying to determine the question below:
Mr. Learnwell wants to setup a scholarship of $4500 paid at the end of every six months. If the interest rate is 6.4% compounded semi-anually, how much must Mr. Learnwell pay into the scholarship fund now.
I've got the formula:
$A = R \cdot \frac{1-(1+i)^{-n}}{i}$
So therefore $A=4500\frac{1-(1+0.032)^{-2}}{0.032} = 8585.72$
I'm not too sure if this is the right formula or answer. Could i get some advice?
The future value ok. : $FV_1=4500\cdot \frac{1.032^2-1}{0.032}$
To get the present value, I would discount the future value once, with a interest rate of $i=0.064$
$PV=4500\cdot \frac{1.032^2-1}{0.032}\cdot \frac{1}{1.064}$
You discounted the future value two times with the semi-annually interest rate of $i_2=0.032$
$\tilde{PV}=4500\cdot \frac{1.032^2-1}{0.032}\cdot \frac{1}{1.032^2}=4500\cdot \frac{1-1.032^{-2}}{0.032}$
I think it is more logical to take the annually interest rate, because the PV is independent from the way the FV come about.