# Math Help - Present value annuity

1. ## Present value annuity

You have two options 1) to receive £300 at Y/E for ever
or
2) receive £400 at Y/E for 25 years

market interest rate is 6%

how do i find the present values?

2. Hello, entrepreneurforum.co.uk!

You have two options
1) to receive £300 at Y/E forever
or
2) receive £400 at Y/E for 25 years

Market interest rate is 6%

How do i find the present values?
Option 1

To receive $300 annually forever, the annual interest must be$300.

If $P$ is the present value, the interest for one year is . $6\%\times P$

. . We have: . $0.06P \:=\:300 \quad\Rightarrow\quad P \:=\:\5000$

Option 2

To receive \$400 annually for 25 years, use the formula: . $P \:=\:A\,\frac{r(1+r)^n}{(1+r)^n-1}$

. . where: . $\begin{Bmatrix}P &=& \text{Present value} \\ r &=& \text{Periodic interest rate} \\ n &=& \text{Number of periods} \\ A &=& \text{Periodic payment} \end{Bmatrix}$

We have: . $P \;=\;400\,\frac{(0.06)(1.06^{25})}{1.06^{25}-1} \;=\;5133.342463 \;\approx\;\5113.34$

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