SOLUTION: please help me find this answer for this question How much should you invest each month in order to have $500,000 if your rate of return is 6.4% compounded monthly and you want

Question 1131198: please help me find this answer for this question
How much should you invest each month in order to have $500,000 if your rate of return is 6.4% compounded monthly and you want to achieve your goal in 40 years?
$
How much interest will you earn?
$
How much should you invest each month in order to have $500,000 if you want to achieve your goal in 20 years?
$
If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
$
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
How much should you invest at the end of each month in order to have $500,000 if your rate of return is 6.4% compounded monthly and you want to achieve your goal in 40 years?

How much interest will you earn?

$225.07

How much should you invest each month in order to have $500,000 if you want to achieve your goal in 20 years?

$1031.82

If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

$946,628.83

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the use of a financial calculator helps to get the answers to these questions.

the one i used online can be found at https://arachnoid.com/finance/

for your first problem, the inputs are::

present value = 0
future value = 500,000
number of time periods = 40 * 12 = 480
interest rate per time period = 6.4 / 12 = .5333333.....
payment are to be made at the end of each time period.

you then click on pmt and the calculator tells you that the monthly payments need to be $225.07.

they are shown as minus because it's money going out from you.

here's the display.

for your second problem, the inputs are the same except for number of time periods, which are 20 * 12 = 240.

you then click on pmt and the calculator tells you that the monthly payments are $1031.82.

they are shown as minus because it's money going out from you.

here's the display.

for your third period, the inputs are:

present value = -500,000
number of time periods = 10 * 12 = 120
interest rate per time period = 6.4 / 12 = .5333333.....
payments per time period = 0

you then click on fv and the calculator tells you that the future value in 10 years is $946,628.83

the present value is entered as minus because it's money going out from you.
the future value is shown as positive because it's money coming back to you.

using my TI-BA-II financnail calculator, i got slightly different results, the difference having to do with rounding in the online calculator.

my TI-BA-II gave me the following results.

for the first problem, monthly payment = 225.0708662 which can be rounded to 225.07.

for the second problem, monthly payment = 1031.821058 which can be rounded to 1031.82.

for the third problem, future value = 946,629.2109 which can be rounded to 946,629.21.

the monthly payments between the online calculator and the TI-BA-II are the same after rounding.

the future value is not.

the reason has to do with internal rounding in the online calculator.
it truncates, or rounds, the interest rate to .533333.

that leads to a different future value because 6.4/12 is really .53333333........

the reason i tell you this is just to clue you in to the fact that you could get different answers depending on the calculator that you use.

which one is more accurate?

in this case, the TI-BA-II gives you the more accurate result.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
please help me find this answer for this question
How much should you invest each month in order to have $500,000 if your rate of return is 6.4% compounded monthly and you want to achieve your goal in 40 years?
$
How much interest will you earn?
$
How much should you invest each month in order to have $500,000 if you want to achieve your goal in 20 years?
$
If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
$

a) Amount to invest each month in order to have $500,000, with ROR being 6.4%, compounded monthly, at the END of 40 years:
b) Earned interest: Difference between amount invested over the 40-year period and the $500,000-goal:
c) Amount to invest each month in order to have $500,000, with ROR being 6.4%, compounded monthly, at the END of 20 years:
d) If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
The above is confusing! Are you talking about the SINGLE total amount invested over the 20-year period ($247,637.05) being invested for 10 years,
or the monthly amount of $1,031.82 being invested over a 10-year period?
If the former, then in 10 years the SINGLE total amount of $247,637.05 will accumulate to $468,840.94 over a 10-year period, with ROR of 6.4%, and monthly compounding.
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