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. a. $391,125.87 c. $397,502.32 b. $395,083.12 d. $401,447.24

Option d)$401,447.24

Step-by-step explanation:

We are given that 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 at rate of 6% compounded annually for 20  years

So first of all we need to find the future value of annuity using the formula as shown below :

Here, FV = future value of annuity

         p = $35000   (annual deposit)

         r is rate = 6% = 0.06

         n = number of compounding = 1 ( as we are compounding annually )

        t = number of years = 20

So plugging in all the values in the formula , we get

Simplifying further , we get

Plugging in the given values in the calculator , we get

FV = $ 1287495.69

So far we have got the Total amount for annuity , from here we need to use the concept of compound interest and find the principal amount to be deposited to get the required total amount of $ 1287495.69

The formula for compound interest when compounded annually is given by:

Here A = 1287495.69  (Total amount required)

         P =   ( principal amount to be deposited to meet the required total amount )

         r = 6% = 0.06

        t = 20

So plugging in all the known values in the formula , we get

simplifying further, we get

so required amount to be deposited is given by :

P = $401,447.24

Hope it was helpful !:)

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