Question

Your aunt wants to retire and has $535,000. She expects to live for another 25 years and to earn 7.5% on her invested funds. How much could she withdraw at the end of each of the next 25 years and end up with zero in the account

Answer 1

Answer:

she will withdraw $47995.21 per annum.

Explanation:

Given : $535 000 that the lady is willing to invest. = Present value

             The rate of return that she will get on this investment is 7.5% = i  

            The number of payments or the period of payments which is 25 years= n

Therefore for this kind of problem we will use the present value annuity formula where we are looking for C the number of payments this person will get per annum in retirement within the further 25 years she will live for , so we will use the below formula for a present value annuity:

$Present value = C[(1-(1+i)^-n)/i)$

 Thereafter we substitute the values as mentioned above and solve for C as we have done a breakdown.

    $535000 = C x [(1-(1+7.5%) ^-25)/7.5%], We compute the value in brackets.

$535000=11.14694586C Then we divide by the coefficient of C both sides to solve for C

$535000/11.14694586= C

C = $47995.21 is the amount that she will receive in 25 equal payments per annum until she dies after her retirement.

 

The reason we have used present value annuity in this problem is because it contains the sum that must be invested now to guarantee the lady that is retiring a payment in future that will be equal and also adjust or cater for the interest rates in all the payments that will be given to her that is why present value annuity formula was used on this problem. When she does her withdrawals at the end of 25 years she will be left with a balance of $0 of her investment.