At age 5, how much would you have to save per month to have $1 million in your account at age 65, if your investment rate was 10% per year? Assume no taxes and compounding on a monthly basis.
I use my TI-83.....
N=(65-5)*12
I%=10%/12
PV=0
PMT=0
FV=1,000,000
I used the solver for PMT
PMT= -21.2302
FINAL ANSWER IS $21.23 per month.....the negative represents a out cashflow
compounding monthly so n = (65 - 5)12 = 720 payments
rate r = .10/12 = . .008333
call investment each month = x
then sinking fund (or amount of an annuity) calculation
x = 1,000,000 * .00833 / [(1.00833)^720-1]
x = 21.27
I used .00833 instead of .1/12 to the accuracy of the calculator, suspect your answer more accurate
thank you
To answer this question, you can use the future value of an ordinary annuity formula. The formula is:
FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)
Where:
FV = Future value (which is $1,000,000 in this case)
PMT = Monthly savings amount
r = Annual interest rate (which is 10% or 0.10 in this case)
n = Number of times interest is compounded per year (which is 12 in this case since compounding is done on a monthly basis)
t = Number of years (which is (65 - 5) = 60 years in this case)
By rearranging the formula and solving for PMT, we can find the monthly savings amount needed to reach a future value of $1,000,000:
PMT = FV * (r/n) / [(1 + r/n)^(n*t) - 1]
Substituting the given values:
PMT = $1,000,000 * (0.10/12) / [(1 + 0.10/12)^(12*60) - 1]
PMT ≈ $21.23
The negative sign in front of the PMT value obtained from the calculator (TI-83) is an indication of cash outflow, which means you would need to save $21.23 per month in order to have $1,000,000 in your account at age 65, assuming a 10% annual interest rate, no taxes, and monthly compounding.