Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1.000 should include the comma ($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).

Businesses deposit large sums of money into bank accounts. Imagine an account with $10 million dollars in it.

﻿﻿﻿How much would the account earn in one year of simple interest at a rate of 2.12%? Round to the nearest cent.

﻿﻿﻿How much would the account earn in one year at 2.12% if the interest was compounded daily? Round to the nearest cent.

C. How much more interest is earned by interest compounded daily compared to simple interest? [

To solve these questions, let's go step-by-step.

### A. Simple Interest Calculation:
The formula for simple interest is:

\[
I = P \times r \times t
\]

Where:
- $ I $ is the interest.
- $ P $ is the principal amount, which is $10,000,000.
- $ r $ is the interest rate, which is 2.12% or 0.0212.
- $ t $ is the time in years, which is 1 year.

Substituting the values into the formula:

\[
I = 10,000,000 \times 0.0212 \times 1 = 212,000
\]

Thus, the simple interest earned in one year is **$212,000.00**.

---

### B. Compound Interest Calculation (Compounded Daily):
The formula for compound interest is:

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

Where:
- $ A $ is the amount (principal + interest).
- $ P $ is the principal amount ($10,000,000).
- $ r $ is the interest rate (2.12% or 0.0212).
- $ t $ is the time in years (1 year).
- $ n $ is the number of compounding periods per year (daily compounding means $ n = 365 $).

Now, substitute the values into the formula:

\[
A = 10,000,000 \times \left(1 + \frac{0.0212}{365}\right)^{365 \times 1}
\]

Let's calculate this.

The compound interest earned in one year with daily compounding is **$214,256.88**.

---

### C. Difference Between Compound and Simple Interest:
To find how much more interest is earned with daily compounding compared to simple interest, we subtract the simple interest from the compound interest.

\[
\text{Difference} = 214,256.88 - 212,000.00 = 2,256.88
\]

Thus, the account earns **$2,256.88** more with daily compounding compared to simple interest.

---

Would you like further details or explanations on any part of this?

Here are 5 related questions:
1. What happens to the compound interest if the interest rate increases to 3%?
2. How does the number of compounding periods per year affect the total interest earned?
3. What is the formula for continuously compounded interest?
4. How much interest would the account earn if the simple interest was calculated over 5 years?
5. What would the interest be if it was compounded quarterly instead of daily?

**Tip:** Compounding frequency plays a significant role in increasing the total interest earned. The more frequent the compounding, the more interest is generated!

Businesses deposit large sums of money into bank accounts. Imagine an account with $10 million dollars in it. How much would the account earn in one year of simple interest at a rate of 2.12%? Round to the nearest cent. How much would the account earn in one year at 2.12% if the interest was compounded daily? Round to the nearest cent. How much more interest is earned by interest compounded daily compared to simple interest?

Learn how to calculate simple and compound interest for a $10 million account at an interest rate of 2.12%. This problem uses key financial concepts such as the simple interest formula and compound interest formula with daily compounding. Find out how much more interest is earned with daily compounding. Perfect for high school students or anyone interested in finance.

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