Question

As part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each year. You need to determine how much money must be deposited earning 6% compounded annually in order to make the annuity payment for 20 years.

Answer 1

The formula for finding present value of an ordinary annuity is:
$PV=P*[\frac{1-(1+i)^{-n}}{i}]$, where P - money to be deposited, i - interest rate, n - number of payments.

So in this case, P = 35000, i = 6 / 100 = 0.06, n = 20.

Now, we have everything needed to determine how much money must be deposited:
$PV=35000*[\frac{1-(1+0.06)^{-20}}{0.06}]=401447.24$

So the answer is $401,447.24.

Answer 2

Use the formula of the present value of annuity ordinary
Pv=pmt [(1-(1+r)^(-n))÷r]
Pv ?
Pmt 35000
R 0.06
N 20 years
Pv=35,000×((1−(1+0.06)^(−20))
÷(0.06))=401,447.24