Studdy AI Logo
Math  /  Algebra

QuestionUse the compound interest formula to compute the total amount accumulated and the interest earned. $7500\$ 7500 for 3 years at 6.5%6.5 \% compounded monthly

Studdy Solution

STEP 1

What is this asking? We need to figure out how much money we'll have after putting $7500\$7500 in a savings account for 3 years with a monthly interest rate of 6.5%6.5\%, and also how much of that total is pure profit. Watch out! The interest rate is *annual*, but it's *compounded monthly*, so we need to adjust it accordingly!

STEP 2

1. Calculate the monthly interest rate.
2. Calculate the total number of times the interest is compounded.
3. Calculate the accumulated amount.
4. Calculate the interest earned.

STEP 3

The **annual interest rate** is 6.5%6.5\%, which we can write as 0.0650.065.
Since there are **12 months** in a year, the **monthly interest rate** is:
0.065/12≈0.005416670.065 / 12 \approx 0.00541667

STEP 4

So, our **monthly interest rate** is approximately 0.005416670.00541667, or around 0.54%0.54\% per month.

STEP 5

The money is invested for **3 years**, and the interest is compounded **monthly**.
This means the interest is compounded 3⋅12=363 \cdot 12 = \mathbf{36} times over the **3-year period**.

STEP 6

Now, let's use the **compound interest formula**:
A=P(1+r/n)ntA = P(1 + r/n)^{nt}Where:
* AA is the **future value** of the investment/loan, including interest.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord