# Deferred Annuity question in description. Thank you.

#### meeps

##### New member
Q: What amount should you invest now if you want to receive payments of \$3000 at the end of each year for 10 years with the receipt of the first payment 4 years from now? Assume that the money earns 5% compounded annually.

I have the answer (20,010.97) but when I am calculating the simple ordinary Annuity: p/y: 1, c/y= 1, n=10, i/y= 5, pmt= 3000, fv=0 and compute FV which is (-23165.20479)

now I have to get the deferred annuity so I have to change n to 3 even though the first payments are 4 years. I just need an explanation of why this is so.

#### tkhunny

##### Moderator
Staff member
You didn't perform the 3-year deferral. Your value is at time 3 (1 year prior to the first payment), not time 0 (the time of the investment).

What do you get from this? 23165.20479 / (1.05^3)

Did you build a time map?

0 (now) - Investment
1
2
3
4 3000
5 3000
6 3000
7 3000
8 3000
9 3000
10 3000
11 3000
12 3000
13 3000

Now, the discounted value map, using the investment date as the focus. v = 1/(1.05)

0 (now) - Investment
1
2
3
4 3,000v^4
5 3,000v^5
6 3,000v^6
7 3,000v^7
8 3,000v^8
9 3,000v^9
10 3,000v^10
11 3,000v^11
12 3,000v^12
13 3,000v^13

That's it.

3,000v^4 + 3,000v^5 + ... + 3,000v^13 = Investment

A little algebra

(3,000v^4)(1 + v + v^2 + ... + v^9) = Investment

Are we getting anywhere? Can you add the stuff in the parentheses?

Never been a fan of the formulaic approach. Build the map and understand what it is you are doing. There is a reason why we study Geometric Series in earlier courses.