SOLUTION: Suppose an individual makes an initial investment of $1000 in an account that earns 7.8%, compounded monthly, and makes additional contributions of $100 at the end of each month fo

Algebra ->  Finance -> SOLUTION: Suppose an individual makes an initial investment of $1000 in an account that earns 7.8%, compounded monthly, and makes additional contributions of $100 at the end of each month fo      Log On


   

Question 1126264: Suppose an individual makes an initial investment of $1000 in an account that earns 7.8%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for the next 5 years (so that the account balance will be reduced to $0). (Round your answers to the nearest cent.)
(a) How much is in the account after the last deposit is made?
(b) How much was deposited?
I got this one right: 15400
(c) What is the amount of each withdrawal?
(d) What is the total amount withdrawn?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i'm not quite so sure you got the first part right.

my calculations indicate that the future value of the investment after 12 years is $26,265.91 and the amount you would receive each month for the following 5 years would be $530.07.

here are my inputs for the first part.

$$$

here is my output for the first part.

$$$

here are my inputs for the second part.

$$$

here is my output for the second part.

$$$

i also did the problem in excel to confirm the answer is correct.

here's the output from the excel analysis.

$$$

$$$

$$$

the remaining balance is 0 at the end of the 5 year withdrawal period, as it should be.

your time periods are in months.

the number of month is equal to the number of years * 12.

the interest rate per month is equal to the interest rate per year divided by 12.

the calculator deals in percents, so 7.8% / 12 = .65%.

the excel spreadsheet deals in rates, so 7.8% / 100 = .078 / 12 = .0065.

the initial investments are made at the end of month 0.

the monthly payment are made at the end of month 1 to 144.

the monthly withdrawals are made at the end of month 1 to 60.

end of month 0 of the withdrawal period is equal to end of month 144 of the investment period.

in other words, the remaining balance at the end of month 144 is immediately
reinvested and becomes the remaining balance at the end of month 0 of the withdrawal period.