2. 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 accountant when the individual retires at the age of 65 if the contributions 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?
Indicate your specific subject in the "School Subject" box, so those with expertise in the area will respond to the question.
He will earn 147521
To calculate the answers to these questions, we need to use the formula for compound interest:
A = P(1 + r)^n
Where:
A = the final amount
P = the initial deposit or principal amount
r = the interest rate per period
n = the number of periods
In this case:
P = $1,500
r = 10% = 0.10
n = the number of years
a) To calculate how much will be in the account when the individual retires at the age of 65, with contributions starting at age 45, we can use the formula with n = 20 (65 - 45):
A = $1,500(1 + 0.10)^20
b) To calculate the additional money in the account if the individual stops making contributions at age 65 but defers retirement until age 70, we can use the formula with n = 25 (70 - 45):
A = $1,500(1 + 0.10)^25
c) To calculate the additional money in the account if the individual continues making contributions but defers retirement until age 70, we can calculate the amount contributed from age 65 to age 70, and then use the formula with n = 20 (70 - 45):
Contribution from age 65 to 70 = $1,500/year * 5 years
Additional money in the account if the contributions continue = Contribution from age 65 to 70 * (1 + 0.10)^20
d) To compare the answers to (b) and (c) and determine the effect of continuing the contributions, you can subtract the amount in b) from the amount in c):
Difference = Amount in c) - Amount in b)
This difference will tell you the additional money gained by continuing to make contributions from age 65 to 70.
Now you can plug in the values and use a calculator to find the exact amounts in each case.