exercices on growth periods and continuous growth

mexx

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May 21, 2006
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15
who can help me?
i haven't already worked on it, because i've no idea how to go about these exercices...

1. Suppose, you deposit $25,000 in an account to accrue interest for 40 years. The account pays 4% compounded annually. 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. Deferred: The income tax on the interest that is earned is paid one lump sum at the end of 40 years.
b. Not Deferred: The income tax on the interest that is earned each year is paid at the end of each year.

2. Which of the following would produce a larger balance? Explain!
a. 4.02% annual interest rate, compounded monthly.
b. 4% annual interest rate, compounded continously.

3. Suppose you deposit $1000 in each of two saving accounts. The interest for the accounts is paid according to the options described in Question 2. How long would it take for the balance in one of the accounts to exceed the balance in the other account by $100? By $100,000?
 
What formulas have they given you for this situation?

Part of the exercise uses the formulas demonstrated to you in your other thread. How far have you gotten in applying those?

Please show specifics. Thank you.

Eliz.
 
number 1)

i calculated the balance of a.
my result is 91517.86099

calculation: 25000(1+(0.04/1))^40 = 120025.5157
so the interest is 95025.5157
then 0.7*95025.5157= 66517.86099
25000+66517.86099 = 91517.86099

is is correct?

now i want so solve b.
but i don't know how to calculate when i have to pay the income tax at the end of each year. whats then the formula?
 
ah, and another question.
number 1.
isn't a = non-deferred and b=deferred?
my teacher wrote it that way..
(we're german, but maths is in english)
 
okay, i could solve the exercices exept for this one:
how can i calculate that?

mexx said:
3. Suppose you deposit $1000 in each of two saving accounts. The interest for the accounts is paid according to the options described in Question 2. How long would it take for the balance in one of the accounts to exceed the balance in the other account by $100? By $100,000?
 
To solve the rest of the exercise, you created formulas for the balances of the accounts. To find the difference in the accounts, subtract the formulas. Set equal to the required minimum difference, and solve.

Eliz.
 
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