# present value

• Oct 7th 2008, 06:18 PM
actsci231
present value
Find the present value to the nearest dollar on January 1 of an annuity which pays $2,500 every month for 10 years. The first payment is due on the next April 1 and the rate of interest is 11% convertible monthly. the answer i got was 24104.02971, can anyone pls help confirm this with steps..thanks • Oct 7th 2008, 06:48 PM Soroban Hello, actsci231! The wording is confusing . . . Quote: Find the present value to the nearest dollar on January 1 ? of an annuity which pays$2,500 every month for 10 years.
The first payment is due on the next April 1 ?
and the rate of interest is 11% convertible monthly.

The answer i got was 24104.02971.
Can anyone pls help confirm this with steps? Thanks

I don't understand the use of dates.
. . And what do they mean by "first payment is due"?

I interpret the problem like this:

We want to collect $2500 per month, starting next month. We will deposit a sum of money (present value) now . . and get 11% interest, compounded monthly. Formula: . $P \;=\;A\cdot\frac{(1+i)^n - 1}{i(1+i)^n}$ . where: . $\begin{Bmatrix}P &=&\text{present value} \\ A &=& \text{amount of payment} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$ We have: . $A = 2500,\;\;i = \frac{11\%}{12} = \frac{0.11}{12},\;\;n = 120$ Hence: . $P \;=\;2500\cdot\frac{\left(1+\frac{0.11}{12}\right) ^{120}-1} {\frac{0.11}{12}\left(1 + \frac{0.11}{12}\right)^{120}} \;=\;181,\!488.1886$ Therefore, we must deposit$181,488 now.

• Oct 7th 2008, 06:53 PM
actsci231
me too i dont the wording...but the january 1 is when he deposits the money, and im assuming the first payment thing is when the interest starts to compound so i did it like

2500 [( v^118 - 1)/(v - 1)]

but im not sure if i did this correctly, thanks for the reply
• Oct 7th 2008, 07:34 PM
jonah
On March 1, one month before the first payment is due, the value of your annuity is
$
A = 2,500 \cdot \frac{{1 - \left( {1 + \tfrac{{.11}}
{{12}}} \right)^{ - \left( {10 \times 12} \right)} }}
{{\tfrac{{.11}}
{{12}}}} \approx \ 181,488.1884
$

which is the same as Soroban’s results.
On January 1, two months before March 1, the present value or the discounted value of your annuity is given by
$
P = A\left( {1 + \tfrac{{.11}}
{{12}}} \right)^{ - \left( {\tfrac{2}
{{12}} \times 12} \right)} \approx \ 178,206.1023
$
• Oct 7th 2008, 08:06 PM
actsci231
but doesnt payment start in april