When Derrick turned age 15, his grandparents put $10,000 into an account that yielded 1.4% interest, compounded quarterly. When Derrick turns 18, his grandparents will give him the money to use toward his college education. How much does Derrick receive from his grandparents on his 18th birthday?

To find out how much Derrick will receive on his 18th birthday, we need to calculate the future value of the $10,000 deposit, which is compounded quarterly at an interest rate of 1.4%.

The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ = the future value of the investment
- $ P $ = the principal amount (initial deposit)
- $ r $ = the annual interest rate (decimal form)
- $ n $ = the number of times the interest is compounded per year
- $ t $ = the time the money is invested for, in years

### Given:
- $ P = 10,000 $
- $ r = 1.4\% = 0.014 $
- $ n = 4 $ (since the interest is compounded quarterly)
- $ t = 18 - 15 = 3 $ years

Now we can substitute these values into the formula:

\[
A = 10,000 \left(1 + \frac{0.014}{4}\right)^{4 \times 3}
\]

Let’s calculate the value of $ A $.Derrick will receive approximately $10,428.18 from his grandparents on his 18th birthday.

Would you like further details on the calculation or have any questions?

Here are 5 related questions for further exploration:
1. How does increasing the interest rate affect the future value?
2. What if the money was compounded annually instead of quarterly?
3. How much would Derrick have received if the account was for 5 years instead of 3?
4. What happens if the interest rate is reduced to 1%?
5. How much would need to be initially invested to give Derrick $12,000 after 3 years?

**Tip:** Always confirm whether interest is compounded quarterly, annually, or monthly, as it affects the growth of an investment significantly.

Learn how to calculate the future value of a $10,000 investment with 1.4% interest, compounded quarterly. Find out how much Derrick will receive for his college fund after 3 years. This step-by-step solution uses the compound interest formula, covering key financial concepts and is suitable for students in Grades 10-12.

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