How much should you deposit right now at 6% compounded monthly so that you can withdraw $1000 each month for 10 years?
thanks in advance!
let's assume the withdrawals are at the end of the month.
present value = 1000(1 - 1.005^-120)/.005
= 90073.45
I believe the formula you want is the present value of an annuity
PV = C * [(1 - (1+r)^-n]/r
Where C = payment per period
r = interest rate per period
n = periods.
PV = 1000 * (1 - 1.005^-120)/.005
= 90,073.45
To determine how much you should deposit right now to be able to withdraw $1000 each month for 10 years, we need to use the formula for the future value of an annuity.
The formula for calculating the future value of an annuity is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity
P is the monthly payment
r is the interest rate per period
n is the total number of periods
In this case, we want to find the present value (P), so we need to rearrange the formula:
P = FV * (r / ((1 + r)^n - 1))
Given:
FV = $1000 (monthly payment)
r = 6% per year (0.06/12 = 0.005 monthly interest rate)
n = 10 years * 12 months/year = 120 months
Now we can substitute the values into the formula and calculate the present value:
P = $1000 * (0.005 / ((1 + 0.005)^120 - 1))
Using a calculator or spreadsheet, evaluate the expression inside the parentheses first, and then multiply by $1000 to get the final answer.