1. Compouind interest

1. A relative has decided to establish a bank account for your newborn daughter that will pay for some of her future college expenses. It is intended that the amount be worth $10,000 18 yrs. from now. Assuming that the account will earn 7.6%, compounded quarterly, how much money should be deposited into the account? 2. After moving to the United States from Europe, the Taylors invested their savings of$4000 into an account earning 7.2% interest, compounded monthly. How much interest was earned by the account during each of the first three months?

2. Originally Posted by tony351
1. A relative has decided to establish a bank account for your newborn daughter that will pay for some of her future college expenses. It is intended that the amount be worth $10,000 18 yrs. from now. Assuming that the account will earn 7.6%, compounded quarterly, how much money should be deposited into the account? 2. After moving to the United States from Europe, the Taylors invested their savings of$4000 into an account earning 7.2% interest, compounded monthly. How much interest was earned by the account during each of the first three months?
For Question 1, assuming that the initial deposit is made on 1/1 of the year, since bank compounding for quarterlies occurs on 3/31, 6/30, 9/30, 12/31 of each year, you want:

$10000 /((1 + (0.076/4))^{72})$

=2579.05

The 7.6% per annum is 1.9%/quarter. 18 full years with 4 quarters per year is 72 quarters

This can be verified running this to check the accumulated balance like a 401(k) that is rolling here -> Balance Roll with Interest

Say it is 1/1/2008 > 1/1/2026 when the balance is collected. Roll up 2579.05 at 7.6% compounded quarterly, which is 1.9% per quarter for 18 years with all 72 credited quarterlies and you will get your 10000.

Question 2:

Compound interest takes the previous balance from the last compounding period. So we do this as follows:

7.2% per annum = 7.2/12 = .6% = .006 per month.

Balance after 3 months = $4000 * (1.006)^3 = 4072.43$

Total Interest Earned = Accumulated Balance - Principal = 4072.43 - 4000 = 72.43

3. First of all, Thanks so much On the second question, to figure each of the first three months meaning month 1, month 2, and month 3, do i need to divide 72.43 by 3? I am looking for 3 answers to this question.

4. Originally Posted by tony351
First of all, Thanks so much On the second question, to figure each of the first three months meaning month 1, month 2, and month 3, do i need to divide 72.43 by 3? I am looking for 3 answers to this question.
Ok, I understand. Here you go:

You want the interest credit column. That is the balance at the beginning of the period times the monthly interest credit of 0.006.

Month 1: 4000(.006) = 24 Therefore, new balance is 4024

Month 2: 4024(.006) = 24.14 Therefore, new balance is 4048.14

Month 3: 4048.14(.006) = 24.29 Therefore, new balance is 4072.43