Find the monthly payment on an annuity at 6% annual interest if the value after 30 years
will be $100,000.
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An annuity is a series of equal payments made at regular intervals. The formula to calculate the monthly payment (PMT) for an annuity is:
PMT = FV / [(1 + r/n)^(nt) - 1] * (r/n)
where:
FV = future value of the annuity
r = annual interest rate
n = number of compounding periods per year
t = number of years
In this case, the future value (FV) is $100,000, the annual interest rate (r) is 6% or 0.06, the number of compounding periods per year (n) is 12 (since it's monthly), and the number of years (t) is 30.
Substituting these values into the formula, we get:
PMT = $100,000 / [(1 + 0.06/12)^(12*30) - 1] * (0.06/12)
Solving this equation gives us the monthly payment for the annuity.
PMT = $100,000 / [(1 + 0.005)^(360) - 1] * 0.005
PMT = $100,000 / [10.2857 - 1] * 0.005
PMT = $100,000 / 9.2857 * 0.005
PMT = $53.79
So, the monthly payment on the annuity would be approximately $53.79.
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