SOLUTION: You deposit $25,000 in an account to accrue interest for 40 years. the account pays 4% compunded anually. Assume that the income tax on the earned interest is 30%. Which of the fol

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Question 257689: You deposit $25,000 in an account to accrue interest for 40 years. the account pays 4% compunded anually. Assume that the income tax on the earned interest is 30%. Which of the following plans produces a larger balance after all income tax is paid?
(A) the income tax on the interest that is earned is paid in one lump sum at the end of 40 years.
or
(B)The income tax on the interest that is earned each year is paid at the end of each year.

i know i am supposed to use the A=P(1+r/n)^nt equation, but im not sure where to put the information.
please help. thank you.
Found 2 solutions by rfer, Theo:
Answer by rfer(16322) (Show Source):
You can put this solution on YOUR website!
A= future value
P=present value
r=interest rate
n= number of compounding periods per year
t=number of years
Does that help?

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
25000 deposited today for 40 years.
pays 4% compounded annually.
income tax on the interest is 30%.

which of the following earns more?

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(A) the income tax on the interest that is earned is paid in one lump sum at the end of 40 years.

if you pay the income tax at the end of the 40 years, then you will pay as follows:

the formula is future worth of a present amount.

that formula is:

f = p * (1+r)^n

f = future value
p = present amount
r = 4% per year divided by 100% = .04 interest rate per year.
n = number of years = 40

formula becomes:

f = 25000 * (1.04)^40

this becomes:

f = 120025.51578

uncle sam takes 30% of the profit and you are left with your original investment plus 70% of the profit.

120025.51578 - 25000 = 95025.5157 * .7 = 66517.86099 + 25000 = 91517.86099 = $91,517.86

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(B)The income tax on the interest that is earned each year is paid at the end of each year.

you earn 4% per year and uncle sam takes 30% of that out each year.

you are netting 4% minus .3 * 4% = 4% minus 1.2% = 2.8% per year.

that's what you are earning each year after uncle sam takes out his share at the end of each year.

same formula applies.

f = p * (1+r)^n

p = 25000
r = 2.8% / 100% = .028 interest rate per year.
n = 40 years.

formula becomes:

f = 25000 * (1.028)^40

this becomes:

f = 75450.92962 = $75,450.93

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you make more money paying uncle sam at the end of the 40 years rather than at the end of each year.

this is because the money that you would have been paying uncle sam each year is sitting in your account earning more money each year.