Question

You are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 30th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 5%, how much must you set aside each year to make sure that you will have $2 million in the account on your 65th birthday?

Answer 1

This question requires application of concept of FV of annuities. If we would have plotted these on a time line, this would have been as:

FV = $2 mil

Let us first calculate the PV of this amount (at t=30), by using our basic TVM function, according to which PV = FV/(1 + r)ⁿ.

PV = 2,000,000/(1 +5%)³⁵

PV = $362,850.57

Now, this value is actually the value of annual payments (ordinary annuity) for 35 years + payment that is made today.

PV of ordinary annuity is mathematically shown as:

Now, according to what we discussed,

P = 20,868.91 --> Answer