Question

You are trying to decide how much to save for retirement. Assume you plan to save $7,000 per year with the first investment made one year from now. You think you can earn 5.0% per year on your investments and you plan to retire in 39 years, immediately after making your last $7,000 investment.

a. If, instead, you decide to withdraw $160,000 per year in retirement (again with the first withdrawal one year after retiring), how many years will it take until you exhaust your savings?

Answer 1

To calculate how many years it will take until you exhaust your savings, use the formula for future value of an ordinary annuity. In this case, it will take approximately 64.39 years until you exhaust your savings.

Step-by-step explanation:

To calculate how many years it will take until you exhaust your savings, we can use the formula for future value of an ordinary annuity:

FV = P * ((1 + r) ^ n - 1) / r

where FV is the future value, P is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, we are making an annual payment of $7,000 for 39 years with an interest rate of 5%. We want to find the number of periods it will take for the future value to be equal to or less than $0:

FV = $0
P = $7,000
r = 5% = 0.05
n = ?

Plugging these values into the formula, we get:

$0 = $7,000 * ((1 + 0.05) ^ n - 1) / 0.05

Simplifying the equation, we have:

1 + 0.05 = (1.05) ^ n

0.05 = (1.05) ^ n - 1

Using logarithms to solve for n:

n = log(0.05 + 1) / log(1.05) ≈ 64.39 years

Therefore, it will take approximately 64.39 years until you exhaust your savings.