Question

As part of your retirement plan, you want to set up an annuity in which a regular payment of $50,000 is made at the end of each year. You need to determine how much money must be deposited earning 4.5% compounded annually in order to make the annuity payment for 20 years. a. $647,553.08 c. $655,355.12 b. $650,396.82 d. $658,210.10

Answer 1

Answer:

650396.82$ must be deposited to make the annuity payment of 50000 for 20 years.

Step-by-step explanation:

Given Periodic payments, PMT=50,000$ every year for 20 years.

And deposited amount is compounded annually with 4.5% interest rate.

And interest rate,$i=\frac{r}{m}= \frac{0.045}{1}=0.045$, where m= number of payments in a year=1 here.

And time period, n=20

The amount deposited is nothing but present value.

Hence PV=$PMT\frac{1-(1+i)^{-n}}{i}$

                =$50000\frac{1-(1+0.045)^{-20}}{0.045}$

                =$650396.823≈$650396.82