Question

To live comfortably in retirement, you decide you will need to save $2 million by the time you are 65 (you are 30 years old today). You will start a new retirement savings account today and contribute the same amount of money on every birthday up to and including your 65th birthday. Using TVM principles, how much must you set aside each year to make sure that you hit your target goal if the interest rate is 5%? What flaws might exist in your calculations, and what variables could lead to different outcomes? What actions could you take ensure you reach your target goal?

Answer 1

a)

To calculate the annuity amount the following formula can be used. As the savings begin today, this is an annuity due.

FV of Annuity due = Annuity ( ( (1 + i)^ n -1 )/ i ) * (1 +i)

2,000,000 = A ( ( ( 1 + 5%) ^ 35 -1 ) / 5%) *(1.05)

2,000,000 = A ( (1.05^35 -1 )/5%)* 1.05

2,000,000 = A (90.3203074)* 1.05

A* 1.05 = 2,000,000/90.3203074

A = $22,143/1.05 = $ 21,088.97 is the savings per year needed to achieve the goal

b)

The major flaw in the calculation is the assumption that interest rates remain constant over the period of savings. This is improbable as interest rates change over the period. So if interest rates rise, the amount at retirement would be much higher than the requirement, in that case a lower savings amount must be contributed and if the interest rates fall vice versa. So savings amount has to be adjusted keeping in move with the change in interest rates.