# Compouind interest

• Apr 2nd 2008, 11:08 AM
tony351
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?
• Apr 2nd 2008, 11:32 AM
mathceleb
Quote:

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
• Apr 2nd 2008, 11:50 AM
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.
• Apr 2nd 2008, 11:58 AM
mathceleb
Quote:

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