How much interest is earned in 5 years on $5,000 deposit in an account paying 4% interest compounded daily?


To calculate the interest earned on a deposit with **daily compounding interest**, we use the formula for compound interest:

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

Where:
- $ A $ = the final amount (principal + interest)
- $ P $ = the initial principal (the amount deposited) = $5,000
- $ r $ = annual interest rate = 4% = 0.04
- $ n $ = number of times the interest is compounded per year = 365 (daily compounding)
- $ t $ = the number of years = 5

The interest earned will be:

\[
\text{Interest} = A - P
\]

Now, let’s calculate this step by step.

### Step 1: Calculate $ A $
\[
A = 5000 \left( 1 + \frac{0.04}{365} \right)^{365 \times 5}
\]

Let's calculate the exact value.The final amount after 5 years will be **$6,106.95**, and the interest earned on the $5,000 deposit will be **$1,106.95**.

Would you like more details or have any further questions?

Here are 5 related questions you might find interesting:
1. What would the interest be if the account compounds quarterly instead of daily?
2. How would the interest change with a 6% interest rate over the same period?
3. What happens to the interest earned if the deposit period is extended to 10 years?
4. How does continuous compounding compare to daily compounding?
5. What is the formula for simple interest, and how does it differ from compound interest?

**Tip:** The more frequently interest is compounded, the more interest you will earn on your deposit.

How much interest is earned in 5 years on $5,000 deposit in an account paying 4% interest compounded daily?

Calculate the interest earned on a $5,000 deposit in 5 years with 4% interest compounded daily. Understand compound interest formulas and finance math concepts. Learn the step-by-step process to find out that the total interest earned is $1,106.95. Suitable for students in Grades 10-12.

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