# Future Value of Annuity

Textbook: If you invest \$2000 a year (at 9%) from ages 31 to 65, these funds will grow to \$470,249 by age 65.

***the textbook did not say how they got this number, I just assumed it used FVA because it is in the same section

My calculation:

FVA = 2000 (( 1.09 )^35 - 1)/0.09)

FVA = 431,421.5093

Not sure if 35 is the correct amount of years, but regardless I did not get the answer from the book. What am I missing?

• Try it with 33,33 years (100/3 years). – Dilip Sarwate Oct 27 '17 at 3:25
• I calculated 370, 727 which is closer I guess – pfmguy Oct 27 '17 at 3:27
• ah im a clutz, i meant \$470,249 – pfmguy Oct 27 '17 at 3:46

Assuming 9% nominal compounded monthly, calculate the effective annual rate `r`.

``````r = (1 + 0.09/12)^12 - 1
c = 2000
n = 35
a = future value
``````

For calculation details see Calculating the Future Value of an Annuity Due.

The above formula is calculated from the summation by induction.

``````∴ a = c (((1 + r)^n - 1)/r) (1 + r) = 470249.45
``````

The future value is \$470,249.45

• Is this not the value at age 66, with no payment made? It seems to be what the questioner wanted, since it matches the expected value exactly, but not what the question asks... – DJohnM Oct 27 '17 at 6:27
• @DJohnM Yes, I found that odd too, but it's the value at the end of the 65th year. – Chris Degnen Oct 27 '17 at 6:41
• From age 31 to age 65 is 34 years, not 35 years, (measured from 31st birthday to 65th birthday) and so, read literally, the OP's textbook is incorrect. As you say, the calculation gives the value at the end of the 65th year (the day before the 66th birthday), assuming that the interest is paid on the last day of the period. – Dilip Sarwate Oct 27 '17 at 15:55