If I make annual deposits of $8700 into a retirement account that pays 10.1% interest compounded monthly, How large will my account balance be in 33 years. Help is greatly appreciated as I cannot figure this out.
Again, sometimes the questions submitted are unclear......If you are taking a test or doing homework, you'll need to justify your answer by stating what the assumptions are
Assumption: the interest rate is 10.1% annually compounded MONTHLY Annual Deposit 8700
10.1% Annual = .84166667 MONTHLY
EFFECTIVE ANNUAL RATE would be (1.0084166667)^12 = 1.10580914922 Corresponding to a 10.580914922% APR
There are books with equations for different scenarios of cash flow analysis and there are calculators for calculating these equations but you MUST know how to use them
For the FUTURE Value (F) of a given ANNUAL payment (A) with discrete compounding (NOT CONTINOUS COMPOUNDING) F = A ( (1+i)^n - 1)/i ) Where n =33 i =.10581 in this problem
Substitute: F = 8700 ( ( (1.10581)^33) -1)/.10582 = $ 2,189,952.30
Engineering Economic analysis was one of the most useful courses I took in Electrical Engineering way back when. It will be VERY important to you in the future to understand the time value of money to be successful at money management/retirement/house buying/investing etc. Good Luck!!
+1975 You need to figure out how much 10.1% interest is, by multiplying 10.1 by 8700
Then, since you're trying to find out how large your account balance will be in years and that interest is monthly, you multiply the interest by 12 and then add that on to 8700
After that, you add up the number you got above, 33 times for the 33 years,
Hopefully this helps! :) I appologize in advance if this in incorrect
If I make annual deposits of $8700 into a retirement account that pays 10.1% interest compounded monthly, How large will my account balance be in 33 years. Help is greatly appreciated as I cannot figure this out.
Given all the above info, you should have saved a staggering $2,189,952.28.
Because the payments are annual, we must convert the interest rate from monthly compound into annual compound: 10.1% / 1200=0.00841666667 +1=1.00841666667^12=1.10580914878 - 1 X 100=
10.580914878%, effective annual rate:
FV=P[((1 + .10580914878)^33 - 1) / .10580914878]
FV=8,700[251.718653073]
FV=$2,189,952.28
Again, sometimes the questions submitted are unclear......If you are taking a test or doing homework, you'll need to justify your answer by stating what the assumptions are
Assumption: the interest rate is 10.1% annually compounded MONTHLY Annual Deposit 8700
10.1% Annual = .84166667 MONTHLY
EFFECTIVE ANNUAL RATE would be (1.0084166667)^12 = 1.10580914922 Corresponding to a 10.580914922% APR
There are books with equations for different scenarios of cash flow analysis and there are calculators for calculating these equations but you MUST know how to use them
For the FUTURE Value (F) of a given ANNUAL payment (A) with discrete compounding (NOT CONTINOUS COMPOUNDING) F = A ( (1+i)^n - 1)/i ) Where n =33 i =.10581 in this problem
Substitute: F = 8700 ( ( (1.10581)^33) -1)/.10582 = $ 2,189,952.30
Engineering Economic analysis was one of the most useful courses I took in Electrical Engineering way back when. It will be VERY important to you in the future to understand the time value of money to be successful at money management/retirement/house buying/investing etc. Good Luck!!
There is yet another method of solving this problem:
Since the payment is annual and the interest rate is compounded monthly, we can convert the annual payment of $8,700 into MONTHLY equivalent payments:
Therefore $8,700 annual payments are equivalent to $692.05 monthly payments. Now we use the same formula used by "Guest #3".
FV=$692.05[(1+.101/12)^(33*12)-1/(.101/12)]
FV=$692.05(3,164.45185109)
FV=$2,189,958.90. The difference between this and "Guest #3" is due to rounding off the payment of $692.05 to two decimal places. Otherwise, the two methods give exact results as in "Guest #3"
