Question

Regarding the question, "Mr. Wilks is 30 years old today and wants to set aside an equal", which formula was used to arrive at the amount that should be in the account at age 60? I started out using the Present Value of Ordinary Annuity but I am stuck after that. I am not sure how to factor in the $550,000. Please bear in mind that I have to show working out and not allowed to use Excel when doing final exams. Could a more detailed, step-by-step solution be given, please? Thank You

Answer 1

To calculate a retirement planning problem without Excel, the steps will be as following:

1. The annual retirement requirement will be the annuity & you can find its PV using the PV of ordinary annuity factor at given rate & duration.

PV = Present Value of ordinary annuity for the duration when retirement income is required

2. Next, if some amount is required to be left in the account as inheritance, the PV of that can be calculated using the PV of single cash flow. For example, if 550,000 is required after 20 years, its present value can be calculated as:   PV= 550,000 / (1 + rate)^20

3. Then you add the above 2 PVs to get the Present Value of the account that will be required at the time of requirement.

4. Once you have the value that will be required at the time of requirement, you just need to find the annuity payment (before retirement) that will yield that future value. For this, you can use the following formula:

​FV of Annuity​= PMT×[((1+i)ⁿ−1​) / i]

where: PMT= Annuity payment = Annual savings required

i=interest rate before retirement

n=number of payments​

The PMT figure calculated by solving the above equation will be the required annual savings

(* If you have any doubt regarding any of the steps or not able to apply, please let me know in the comments)