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

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

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=(r)/(m)= (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(1-(1+i)^(-n))/(i)`

=
`50000(1-(1+0.045)^(-20))/(0.045)`

=$650396.823≈$650396.82