SOLUTION: You plan to invest $600 in your savings account this year and then you intend to increase the amount that you invest by 3% each year. If you invest in a savings account each that e

Question 1124067: You plan to invest $600 in your savings account this year and then you intend to increase the amount that you invest by 3% each year. If you invest in a savings account each that earns an effective annual interest rate of 7% how much money will you have in your account in 18 years?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
my calculations are shown in the following spreadsheet printout.

$$$

based on this printout, the amount of money at the end of year 18 will be 26,923.86239.

please note that the end of year 0 is the beginning of year 1.
this follows through to the end where the end of year 17 is the beginning of year 18.

investments are made at the beginning of year 1 to the beginning of year 18.

this is equivalent to investments being made at the end of year 0 to the end of year 17.

each year, the investment is increased by 3%.

that's shown in column E of the printout.

the remaining balance at the end of each year is shown in column G of the printout.

the procedure for calculating the remaining balance is as follows:

the remaining balance at the end of year 0 is 600.

that's the amount that was made at the beginning of year 1 which is also the end of year 0 as noted above.

at the end of year 1, the remaining balance at the end of year 0 is multiplied by 1.07 and then the investment at the end of year 1 is added to it to form the remaining balance at the end of year 1.

the calculation would be 600 * 1.07 + 618 - 1260.

at the end of year 2, the remaining balanced at the end of year 1 is multiplied by 1.07 and then the investment at the end of year 2 is added to it to form the remaining balance at the end of year 2.

the calculation would be 1260 * 1.07 + 636.54 = 1984.74.

this continues all the way to end.

at the end of year 18, the remaining balance at the end of year 17 is multiplied by 1.07 and then the investment at the end of year 18 is added to it to form the remaining balance at the end of year 18.

the calculation would be 25162.48822 * 1.07 + 0 = 26923.8624.

there is 0 investment at the end of year 18 because the last investment was made at the end of year 17 which is also the beginning of year 18.

note that 26923.8624 manually calculated versus 26923.86239 in the excel spreadsheet is because of rounding differences between the numbers displayed by the excel spreadsheet and the numbers stored internally in the excel spreadsheet.

the calculator used the displayed number while the excel spreadsheet used the internally stored number which is rounded to many more decimal digits than shown.

if you round your answer to two decimal digits, it will be the same at $26,923.86.

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