Math Question?

Question

If $12,000 is deposited quarterly into an IRA account paying 5.25% compounded quarterly, find the amount in the account after 15 years if the deposits are made at the end of each 3-month period.

The answer by Charles R. is wrong, not even close.

Answer 1

Assuming you mean $12K/yr, or $3K/qtr, you'd have either $274,798 if you started say Dec 31 and contributed for 15 yrs. This would not include the $3000 made on Dec 31st after the 15 yrs.

Or you'd have $271,237 if you deposited your first payment say on March 31st and contributed 59 more times at the end of the quarters. You get no interest that first quarter from Jan 1 to March 31 since no monies are deposited yet. And on the last payment Dec 31st of the last year, it's still worth $3000 since it's your last day.

Most likely the $274,798 is what you're looking for.

Hope that helps!

Answer 2

Given the information you provided, I get exactly the same answer the first responder gave. If you know that's wrong, then we must be interpreting the information you provided differently than you intended.

I read it to mean that $12,000 is going to be put into an IRA account on the last month of every quarter (which would be $48,000 for the year - a completely unrealistic value since that's way above the maximum allowed contribution to an IRA) and that the interest rate is 5,25% per year, compounded quarterly (which means 1.3125% paid on the last day of each quarter - the same day that the deposits are made). I also read the "15 years" to mean 60 quarters, with the last deposit being made on the last day of the period (and therefore earning no interest). Using those assumptions, I also got $1,084,949.37.

Taking some guesses at what you wrote that we read differently than you meant it...

If you really meant $12,000 per YEAR, with $3,000 each quarter, then the final value would be $271,237.34.

If you really mean 5.25% interest every quarter (which seems unrealistic) with $12,000 per quarter, then it's $4,695,770.64.

If you meant 15 years starting with the date of the first deposit (which is at the very end of a quarter) with $12,000 per quarter and 5.25% per year, then it would be $1,111,189.34
if you include a 61st deposit on the last day of the period, or $12000 less if you don't.

If none of those is what you meant, then I guess we need more clarification.

Answer 3

the answer is $1,084,949.37

The formula from MS excel is
+FV(A3/A4,A4*A5,-A2,0,0)

WHERE:
A2 = 12,000
A3 = 5.25%
A4 = 4
A5 = 15