Question

General MathematicsProblem:What sum would have to be invested at 9% conpounded annually to provide an ordinary annuity at ₱8,000 per year for 5 years?

Answer 1

Given that a future value annuity of 8,000 is accrued at 9% compounded annually, the present value of the annuity is evaluated as

`\begin{gathered} PV=P((1-(1+r)^(-n))/(r))\text{ ----- equation 1} \\ \text{where } \\ PV\text{ }\Rightarrow present\text{ value of the annuity} \\ P\Rightarrow value\text{ of each payment} \\ r\Rightarrow interest\text{ rate} \\ n\Rightarrow period \end{gathered}`

Thus,

`\begin{gathered} P=8,000 \\ r=9\text{\%}=(9)/(100)=0.09 \\ n=5 \\ PV\text{ is unknown} \\ \end{gathered}`

Substitute the above value into equation 1, to solve for PV

`\begin{gathered} PV\text{ = 8000(}(1-(1+0.09)^(-5))/(0.09)) \\ \Rightarrow8000*(1-1.09^(-5))/(0.09) \\ =31117.21 \end{gathered}`

Hence, the sum to be invested is 31117.21