a. To determine how much will be in the account when the individual retires at age 65 if the savings program starts when the person is age 40, we can use the future value of an annuity formula:
FV = P * [(1 + r)^n - 1] / r
where FV is the future value of the account, P is the annual deposit amount, r is the interest rate, and n is the number of years.
In this case, P = $3,000, r = 0.08, and n = 65 - 40 = 25 years.
FV = $3,000 * [(1 + 0.08)^25 - 1] / 0.08
FV ≈ $3,000 * [8.1452] ≈ $244,356
So there will be approximately $244,356 in the account when the individual retires at the age of 65.
b. To find out how much additional money will be in the account if the saver defers retirement until age 70 and continues the contributions, we can recalculate the future value of the account with n = 70 - 40 = 30 years.
FV = $3,000 * [(1 + 0.08)^30 - 1] / 0.08
FV ≈ $3,000 * [10.819] ≈ $324,573
The additional money in the account is the difference between the future values when retiring at age 70 and age 65:
Additional money = $324,573 - $244,356 ≈ $80,217
So, there will be approximately $80,217 additional money in the account if the saver defers retirement until age 70 and continues the contributions.
c. To find out how much additional money will be in the account if the saver discontinues the contributions at age 65 but does not retire until age 70, we need to calculate the future value of the account at age 65 and then calculate the future value of that amount after five more years without contributions.
First, we already calculated the future value at age 65 in part a, which is $244,356.
Now, we can calculate the future value of that amount after 5 more years without contributions using the compound interest formula:
FV = P * (1 + r)^n
In this case, P = $244,356, r = 0.08, and n = 5 years.
FV ≈ $244,356 * (1 + 0.08)^5 ≈ $358,811
The additional money in the account is the difference between the future values when retiring at age 70 without contributions and age 65:
Additional money = $358,811 - $244,356 ≈ $114,455
So, there will be approximately $114,455 additional money in the account if the saver discontinues the contributions at age 65 but does not retire until age 70.
A self-employed person deposits $3,000 annually in a retirement account (called a Keogh account) that earns 8 percent.
a. How much will be in the account when the individual retires at the age of 65 if the savings program starts when the person is age 40?
b. How much additional money will be in the account if the saver defers retirement until age 70 and continues the contributions?
c. How much additional money will be in the account if the saver discontinues the contributions at age 65 but does not retire until age 70?
1 answer
1 answer