Carmen is planning to invest $200 in a retirement account at the beginning of each month for the next 20 years. The account is earning 3.15% interest, compounded annually. He used the following formula and variables to solve for the future value of the account after 20 years.

FVOA = Future Value of an Ordinary Annuity
C = 2400
n = 1
t = 20
i = 0.0315

He found that the future value of this account will be $65481.95. Is Carmen’s solution correct? If not, explain what he did wrong and provide the correct solution.

Question

Carmen is planning to invest $200 in a retirement account at the beginning of each month for the next 20 years. The account is earning 3.15% interest, compounded annually. He used the following formula and variables to solve for the future value of the account after 20 years. 



FVOA = Future Value of an Ordinary Annuity
C = 2400
n = 1
t = 20
i = 0.0315

He found that the future value of this account will be $65481.95. Is Carmen’s solution correct? If not, explain what he did wrong and provide the correct solution.

dumbcow · Answer

yes the solution is correct...i just checked with a financial calculator
do you need all the math laid out...its more geometric series

anonymous · Answer

My answer for this problem is different. Annuity Due payments are to be treated with BGN mode. The other part is that the interest rate must be calculated on a Monthly basis to relate to the impact on interest accumulation will have on the of payments made at different times during the year. Example

N=20*12=240
I=3.15% / 12 = 0.2625%
PMT=200
PV=0

FV= 66747.5338
one of my main questions to solving this problem, they stated it was annually but also that it was invested at the beginning of each month. I used annually and simply examined the other information as in which formula to use. Since it was the beginning, FVOA was correct. What i didn't get was where the 2400 came from? Wouldn't C have been 200

dumbcow · Answer

ahh right but the fact it is compounded annually not monthly i just assumed it was equivalent to 20 yearly payments of 2400

dumbcow · Answer

if they give interest at end of year

anonymous · Answer

so am i correct or are you?

dumbcow · Answer

well you are correct if interest is compounded monthly...however, it states interest is compounded annually

anonymous · Answer

i dunnno what i shud do :(

dumbcow · Answer

not 100% but pretty sure solution given is correct...this is like a trick question they are giving you unnecessary information (fact that deposits made beginning of month)
when bank calculates interest at end of each year, they look at balance
so 12 $200 deposits is same as 1 $2400 deposit

does that help

anonymous · Answer

yeah, im going to say that the solution is correct