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.
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Using FVoa = PMT [((1 + i)n - 1) / i]
FVoa = 2400 [((1 + 0.0315)^20 - 1) / 0.0315]
I get the same answer. Assuming it's correct.
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
I=3.15% / 12 = 0.2625%
Hope this explains the logic.
But the interest is still compounded annually? Wouldn't it state if it were compounded per month
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That was 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?
Think about the payment made at the starting of the year compared to the last. The interest received on the January payment is not the same as that in December. Which is why I treated each payment with monthly interest rates, instead of an annualized rate. The difference in our answers come from minute incremental affect of compounded interest.
Hope this helps :)
even better though is you could treat it as a 2-step calculation.
1) Calculate the FV of 1 year of monthly payments, with interest at the end
2) plug this amount into the calculation of 20 yearly payments, with interest paid yearly.