# Finance annuity problem

• Apr 6th 2008, 09:46 AM
tony351
Finance annuity problem
When lisa was first hired by the EPA, she had sufficient income to deposit $600 each quarter into an IRA paying 10% interest, compounded quarterly. The quarterly deposits last for 12 years. a. How much was in the account at the end of 12 years? b. Because of her parents nursing home costs, Lisa was not able to continue the deposits. Instead she deposited the entire IRA account into a 30 year certificate of deposit earning 12% compounded monthly. What was the value of the account when it matured? • Apr 6th 2008, 12:13 PM mathceleb Quote: Originally Posted by tony351 When lisa was first hired by the EPA, she had sufficient income to deposit$600 each quarter into an IRA paying 10% interest, compounded quarterly. The quarterly deposits last for 12 years.
a. How much was in the account at the end of 12 years?
b. Because of her parents nursing home costs, Lisa was not able to continue the deposits. Instead she deposited the entire IRA account into a 30 year certificate of deposit earning 12% compounded monthly. What was the value of the account when it matured?

Answer a) is 54,515.75 assuming payments are at the end of the quarter. Go here:

Annuity Immediate Accumulated Value

Since we are on a quarterly compounding versus an annual interest rate, our interest rate is 2.5% per quarter. 10/4 = 2.5.

For question b, we want to roll up that balance for 30 years at 12% per year compounded monthly.

Go here: Balance Roll with Interest

Your starting balance is question a. Interest rate is 12, and make your dates a 30 year span. I did 1/1/2008 to 1/1/2038. I got an answer of 1,959,821.66 using monthly compounding which is what your problem gives. This is just the 1% rate for 360 months as you see in the math. Let me know if you have questions.
• Apr 6th 2008, 02:38 PM
tony351
The answer is correct but when i try and use the formula I get a totally different number, A much smaller number. If you can, explain to be the formula to use!! Thanks for your help:)
• Apr 6th 2008, 04:36 PM
mathceleb
Quote:

Originally Posted by tony351
The answer is correct but when i try and use the formula I get a totally different number, A much smaller number. If you can, explain to be the formula to use!! Thanks for your help:)

The formula is $\displaystyle AV = Pmt * s_{\bar n|i}$ where $\displaystyle s_{\bar n|i} = ((1 + i)^n - 1)/i$

where i = 0.025, n = (10*4) = 40, Pmt = 600. Just like the math on my site says, we get our number. In your book, it should be called the "Accumulated Value of an Annuity Immediate".

For Part ii, it's $\displaystyle AV = Balance * (1 + i)^n$

where Balance = 54515.75, n = (12*30) = 360.

If you are using my site, interest rates are entered as whole, not divided by 100. For the first problem, enter i as 2.5. The second problem, enter 12, the calculator will divide it into monthly pieces which will be 1%.

Which part is troubling you? Did you use 30 for n instead of 360 on part B?

Also, to see how that annuity formula for question a is derived, check out Soroban's derviation post here:

http://www.mathhelpforum.com/math-he...nuation-2.html