posted by matt on .
Mr. Jones intends to retire in 20 years at the age of 65. As yet he has not provided for retirement income, and he wants to set up a periodic savings plan to do this. If he makes equal annual payments into a savings account that pays 4 percent interest per year, how large must his payments be to ensure that after retirement he will be able to draw $30.000 per year from this account until he is 80?
This problem must be broken into two parts to solve. First, the present value of the
retirement annuity must be calculated.
Now we need to calculate the annual savings required that will grow to this retirement
amount using the future value of an annuity table.
I have to assume that the interest rate stays the same at 4% per annum
the "amount" of an annuity of 20 payments of $x = "present value" of an annuity of $30000 for 15 years
x(1.04^20 - 1).04 = 30000(1 - 1.04^-15)/.04
x(1.04^20 - 1) = 30000(1 - 1.04^-15)
x = 11201.25