SOLUTION: Nicky is 45 years old.he plans to retire when he is 62.he has opened a retirement account that pays 4.25% interest compound monthly.if he makes monthly deposit of 300$ how much wil
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-> SOLUTION: Nicky is 45 years old.he plans to retire when he is 62.he has opened a retirement account that pays 4.25% interest compound monthly.if he makes monthly deposit of 300$ how much wil
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Question 867543: Nicky is 45 years old.he plans to retire when he is 62.he has opened a retirement account that pays 4.25% interest compound monthly.if he makes monthly deposit of 300$ how much will he have on the account by the time he retires Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the annual interest rate is .0425.
the monthly interest rate is .0425 / 12 = .003541667
the number of years is equal to 62 - 45 = 17.
the number of months is equal to 12 * 17 = 204.
his monthly deposits are assumed to be deposited at the end of each month.
the formula is for the future value of a series of payments that are paid at the end of each month.
interest is calculated at the end of each month and is reinvested as principal.
the formula for the future value of a series of payments is shown below:
fv = future value
pmt = payment per time period
i = interest rate per time period
n = number of time periods
the time periods are months in this problem.
in your problem:
n = 204 months
i = .003541667 per month
pmt = 300 per month
the formula becomes:
stick that in your calculator and solve to get:
fv = $89,529.76
this agrees with the number i previously calculated using a financial calculator so i'm confident the number is good.
if you want to see how the monthly transactions work out, i used excel to create the monthly payments and balance for you.
that is shown below:
n pmt int bal
0 0 0 0
1 300 0 300
2 300 1.0625 601.0625
3 300 2.128763021 903.191263
4 300 3.19880239 1206.390065
5 300 4.272631482 1510.662697
time points 6 to 198 have been deleted..................
199 300 304.1325346 86476.84819
200 300 306.2721707 87083.12036
201 300 308.4193846 87691.53975
202 300 310.5742033 88302.11395
203 300 312.7366536 88914.8506
204 300 314.9067626 89529.75737
at time point 0 he has nothing in the account.
at time point 1 (end of month 1) he deposits 300 and his balance is 300.
at time point 2 he earns interest on the 300 balance from time point 1 plus he adds another 300 payment to get a balance of 601.
at time point 3 he earns interest on the 601 balance from time point 2 plus he adds another 300 payment to get a balance of 903.
this goes on until time point 204 when he makes the last payment.
