At the end of each year a self-employed person deposits $1,500 in a retirement account that earns 10 percent annually. a) How much will be in the account when the individual retired at the age of 65 if the contribution start when the person is 45 years old? b) How much additional money will be in the account if the individual stops making the contribution at age 65 but defers retirement until age 70? c) How much additional money will be in the account if the individual continues making the contribution but defers retirement until age 70? d) Compare the answers to (b) and (c) What is the effect of continuing the contributions? How much is the difference between the two answers?

Question

At the end of each year a self-employed person deposits $1,500 in a retirement account that earns 10 percent annually. a) How much will be in the account when the individual retired at the age of 65 if the contribution start when the person is 45 years old? b) How much additional money will be in the account if the individual stops making the contribution at age 65 but defers retirement until age 70? c) How much additional money will be in the account if the individual continues making the contribution but defers retirement until age 70? d) Compare the answers to (b) and (c) What is the effect of continuing the contributions? How much is the difference between the two answers?

Answer 1

To answer these questions, we need to calculate the future value of the retirement account based on the yearly contributions and the interest rate. We will be using the formula for the future value of an annuity.

The formula for the future value of an annuity is:
FV = P * ((1 + r)^n - 1) / r

Where:
FV = Future Value
P = Yearly contribution
r = Interest rate per period (in this case, 10% or 0.1)
n = Number of periods

a) To determine the future value of the retirement account when the individual retires at age 65 with contributions starting at age 45, we have:
P = $1,500
r = 0.1
n = 65 - 45 = 20 (since the contributions start at age 45 and end at age 65)

Using the formula, we can calculate:
FV = $1,500 * ((1 + 0.1)^20 - 1) / 0.1

b) To find the additional money in the account if the individual stops making contributions at age 65 but defers retirement until age 70, we need to calculate the future value with a new time period.
P and r remain the same, but n changes to 70 - 45 = 25.

FV = $1,500 * ((1 + 0.1)^25 - 1) / 0.1

c) To determine the additional money in the account if the individual continues making contributions and defers retirement until age 70:
P and r remain the same, but n changes to 70 - 45 = 25.

FV = $1,500 * ((1 + 0.1)^25 - 1) / 0.1

d) To compare the answers for b) and c), we need to find the difference in the future values:
Difference = FV of c) - FV of b)

By subtracting the value found in b) from the value found in c), we can determine the effect of continuing contributions until age 70.

Let's calculate the values using these formulas to find the answers.