Compound Amount Question

Question

Every year for 3 years, a person deposits $5,000 in an account which pays at a 4.5% annual interest rate compounded quarterly. After the end of the third year, the person leaves the compound amount in the bank for another five years under the same terms. How much is in the account at the end?

Answer 1

You could look at each deposit separately:

1st is compounded 8 years (compounded quarterly): 5000*(1 + .045/4)^(8*4) = 7152.26

2nd is compounded 7 years (compounded quarterly): 5000*(1 + .045/4)^(7*4) = 6839.26

3rd is compounded 6 years (compounded quarterly): 5000*(1 + .045/4)^(6*4) = 6539.96

Add them up for the total.

Answer 2

To calculate the final amount in the account, you'll need to break this problem down into two parts:

1. Calculate the amount after 3 years of annual deposits and quarterly compounding.
2. Calculate the amount after 5 more years with the existing balance and quarterly compounding.

Let's tackle the first part:

1. Calculate the future value of the deposits after 3 years with quarterly compounding. The formula for compound interest is:
2. A = P(1 + r/n)^(nt)
3. Where:
4. A is the future value of the investment/loan, including interest.
5. P is the principal amount (the initial deposit or balance).
6. r is the annual interest rate (in decimal form).
7. n is the number of times that interest is compounded per year.
8. t is the number of years.
9. In your case, P = $5,000, r = 4.5% or 0.045, n = 4 (quarterly compounding), and t = 3 years.
10. A = 5000(1 + 0.045/4)^(4*3) A = 5000(1 + 0.01125)^12 A = 5000(1.01125)^12 A ≈ 5000 * 1.139618159
11. A ≈ $5,698.09 (rounded to the nearest cent)

After 3 years of annual deposits with quarterly compounding, the account balance is approximately $5,698.09.

Now, let's move on to the second part:

1. Calculate the amount after 5 more years of leaving the balance in the account with quarterly compounding.
2. Now, P is the balance from the previous step, which is approximately $5,698.09. We keep the same interest rate, compounding frequency, and use t = 5 years.
3. A = 5,698.09 * (1 + 0.045/4)^(4*5) A = 5,698.09 * (1.01125)^20
4. A ≈ 5,698.09 * 1.24224181
5. A ≈ $7,081.20 (rounded to the nearest cent)

So, after leaving the compound amount in the bank for another five years under the same terms, there will be approximately $7,081.20 in the account at the end.