SOLUTION: Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time. ​$369 per month

Algebra ->  Finance -> SOLUTION: Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time. ​$369 per month      Log On


   

Question 1118323: Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time.
​$369 per month invested at 4​%, compounded​ monthly for 7 years;
then ​$603 per month invested at 6​%, compounded​ monthly, for 7 years.
What is the amount in the account after 14 ​years?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
$369 per month invested at 4​%, compounded​ monthly for 7 years;
then ​$603 per month invested at 6​%, compounded​ monthly, for 7 years.
What is the amount in the account after 14 ​years?

i am assuming that the future value of the first investment at 4% is then reinvested for the next 7 years at 6% on top of the new investment at 6%.

this is what i found.

i used the following online calculator to come up with the answer i think you are looking for.

https://arachnoid.com/finance/

https://arachnoid.com/finance/

here's my input for the first loan.

$$$

here's the output for the first loan.

$$$

here's my input for the second loan.

$$$

here's my output for the second loan.

$$$

now i have the future value of both loans.

the first loan, however, needs to be brought forward another 7 years at 6% a year compounded monthly in order to have the total value at the end of 14 years.

here's my input for the investment of the future value of the first loan for another 7 years at 6% per year compounded monthly.

$$$
here's my output for the investment of the future value of the first loan for another 7 years at 6% per year compounded monthly.

$$$

the first loan gave me the future value of the payments of 369 at the end of each month for 84 months at 4% per year compounded monthly.

that future value was 35,702.28.

the second loan gave me the future value of the payments of 603 at the end of each month for 84 months at 6% per year compounded monthly.

the future value was 62,756.58.

the 35702.28 future value of the first loan was then invested for another 7 years at 6% compounded monthly.

the future value of that investment ws 54,280.66.

the total value at the end of 14 years was the sum of 54,280.66 + 62,756.58 = 117,037.24.

i also did the problem in excel and this is what i found.

$$$

$$$

$$$

the excel month by month calculations agree with the solution provided by the calculator.