# Math Help - Deferred Annuity problem

1. ## Deferred Annuity problem

I need help answering this problem:

A sequence of 8 annual payments of $750 each, with the first payment due at the beginning of the 6th year; money is worth 6%. (The beginning of year 6 is the end of year 5.) Find the present value. This is my answer: 750 [ (1-1.06^-13) / .06 ] - 750 [ (1-1.06^-5) / .06 ] =$3,480.24

that'll give you a present value (loan proceeds) of $4,657. Now just get present value of that today: 4657 / 1.06^4 = 3689 9. ## Re: Deferred Annuity problem My attachment shows this method, except for the payments. 10. ## Re: Deferred Annuity problem It looks like you're using the formula for an annuity immediate (when interest is applied at the end of the year), rather than for an annuity due (when interest is applied at the beginning of the year). The formula should be $\"{a}_{n,i}=\frac{1-\frac{1}{1+i}^{n}}{\frac{i}{1+i}}$ So, what you typed should look like this: 750 [[ (1-1.06^-13) / .06 ]/1.06] - 750 [[ (1-1.06^-5) / .06 ]/1.06]=3,689.0544 I hope that helps. 11. ## Re: Deferred Annuity problem I took a different approach to a solution: I used Excel and created a simple timeline of 12 periods, populating zero into the first four, and 750 in periods five through twelve, thus representing four time-periods with zero payments, followed by eight with$750.

I then used the NPV function with a 6% rate, and the stream of cash flows (Note: with the first 750 entered in period 5, this is assuming payment at the END of the 5th period {or the beginning of #6})

The NPV evaluates to \$3,689.05; the same as the text book.

To Amul28's comment about Euros vs Dollars, it wouldn't matter as long as the same units are used throughout...

12. ## Re: Deferred Annuity problem

FYI, copying and pasting that formula into Wolfram Alpha results in a valuation of 3,283.24

Originally Posted by downthesun01
The formula should be

$\"{a}_{n,i}=\frac{1-\frac{1}{1+i}^{n}}{\frac{i}{1+i}}$

So, what you typed should look like this:

750 [[ (1-1.06^-13) / .06 ]/1.06] - 750 [[ (1-1.06^-5) / .06 ]/1.06]=3,689.0544