What is the present value of an immediate annuity over 12 years with 4 yearly payments and an interest of i = 2%?

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See the question above, the result should be 10.689. I tried using the temporary annuity-due formula (see below):

$$ \ddot{\mathbf{a}}_{n}^{[m]}=\frac{1-v^{n}}{d^{[m]}} $$

where:

$$ d^{[m]}=m \cdot\left[1-(1+i)^{-\frac{1}{m}}\right] $$

Thanks for any advice.

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You have forgotten to post the value of the annuity. Nevertheless I show you how to deal with this problem. You have an interest rate of $2\%$ p.a. Now you have to convert the yearly interest rate into a quaterly interest rate ($i_4$). This can be done by dividing the yearly interest rate by 4.

$$i_4=\frac{i}4=\frac{0.02}4=0.005$$

In general the present value of an immediate annuity $r$ over $n$ years and a period interest rate of $i_m=\frac{i}{m}$ is

$$PV=r\cdot \left(1+\frac{i}{m}\right)\cdot \frac{\left(1+\frac{i}{m}\right)^{m\cdot n}-1}{\frac{i}{m}\cdot \left(1+\frac{i}{m}\right)^{m\cdot n}}$$

In your case it is

$$PV=r\cdot 1.005\cdot \frac{1.005^{4\cdot 12}-1}{0.005\cdot 1.005^{4\cdot 12}}=r\cdot 1.005\cdot \frac{1.005^{48}-1}{0.005\cdot 1.005^{48}}$$

My guess is that the annuity is $250$.