Question

Suppose that your retirement account has reached a value of $565,651 at age 60. If you let the funds remain invested an EAR of 6.7% until age 65, and do not make further contributions, how much can you receive annually in perpetuity (at the end of the year) starting at end of the year at age 65?

 

Answer 1

To calculate the amount that can be received annually in perpetuity starting at age 65, we can use the perpetuity formula:

PV = PMT / r

where PV is the present value of the perpetuity, PMT is the annual payment, and r is the discount rate.

In this case, we know that the retirement account has a value of $565,651 at age 60, and we want to find the annual payment that can be received starting at age 65. So we need to determine the present value of the perpetuity at age 65.

The discount rate is given by the effective annual rate (EAR) of 6.7%. To convert this to a periodic rate, we use the formula:

r = (1 + EAR/n)^n - 1

where n is the number of compounding periods per year. Since the problem does not specify the compounding frequency, we can assume it is annually. Therefore:

r = (1 + 0.067/1)^1 - 1 = 0.067

Now we can use the perpetuity formula:

PV = PMT / r

To solve for PMT, we rearrange the formula:

PMT = PV x r

We know that PV is $565,651, so:

PMT = $565,651 x 0.067 = $37,922.62

Therefore, the amount that can be received annually in perpetuity starting at age 65 is $37,922.62, assuming the funds remain invested at an EAR of 6.7% and no further contributions are made.

the amount that can be received annually in perpetuity starting at age 65 is $37,922.62,