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
Hello, actsci231!
The wording is confusing . . .
I don't understand the use of dates.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
. . 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: .. where: .
We have: .
Hence: .
Therefore, we must deposit $181,488 now.
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
On March 1, one month before the first payment is due, the value of your annuity is
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
^{ - \left( {\tfrac{2}<br />
{{12}} \times 12} \right)} \approx \$ 178,206.1023<br />
)
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