If $15,000 is invested in an account for 15 years. Calculate the *total interest earned* at the end of 15 years if the interest is:

(a) 8% simple interest: $

(b) 8% compounded annually: $

(c) 8% compounded quarterly: $

(d) 8% compounded monthly: $

Round your answers to the nearest cent.

Question HelpQuestion 9:

Video1

Let's break down each part of the problem and calculate the total interest earned in each case.

### Given:
- Principal $ P = 15,000 $
- Rate $ r = 8\% = 0.08 $
- Time $ t = 15 $ years

---

### (a) 8% Simple Interest

Simple Interest (SI) is calculated using the formula:

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

Substituting the values:

\[
I = 15,000 \cdot 0.08 \cdot 15
\]

Let me calculate that.

---

### (b) 8% Compounded Annually

For compound interest, the formula is:

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

Where:
- $ A $ is the final amount,
- $ n $ is the number of times interest is compounded per year.

For compounding annually, $ n = 1 $. So the formula becomes:

\[
A = 15,000 \left(1 + 0.08\right)^{15}
\]

The total interest earned is $ I = A - P $.

Let me calculate that.

---

### (c) 8% Compounded Quarterly

For quarterly compounding, $ n = 4 $. The formula becomes:

\[
A = 15,000 \left(1 + \frac{0.08}{4}\right)^{4 \cdot 15}
\]

The total interest earned is $ I = A - P $.

Let me calculate that.

---

### (d) 8% Compounded Monthly

For monthly compounding, $ n = 12 $. The formula becomes:

\[
A = 15,000 \left(1 + \frac{0.08}{12}\right)^{12 \cdot 15}
\]

The total interest earned is $ I = A - P $.

Let me calculate that.Here are the total interest amounts calculated for each case:

- **(a) 8% Simple Interest:** \$18,000.00
- **(b) 8% Compounded Annually:** \$32,582.54
- **(c) 8% Compounded Quarterly:** \$34,215.46
- **(d) 8% Compounded Monthly:** \$34,603.82

These values are rounded to the nearest cent.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the formula for compound interest and how is it derived?
2. How does increasing the frequency of compounding affect the total interest earned?
3. What happens if the interest rate is higher or lower than 8%?
4. How does the principal amount influence the total interest in simple and compound interest?
5. How would continuous compounding at 8% over 15 years compare to monthly compounding?

**Tip:** Compounding more frequently results in higher interest, as interest is calculated on a growing balance more often.

If $15,000 is invested in an account for 15 years. Calculate the *total interest earned* at the end of 15 years if the interest is: (a) 8% simple interest: $ (b) 8% compounded annually: $ (c) 8% compounded quarterly: $ (d) 8% compounded monthly: $. Round your answers to the nearest cent.

Find the total interest earned on a $15,000 investment over 15 years at 8% interest, including simple interest and compound interest compounded annually, quarterly, and monthly. Step-by-step solutions provided with detailed formulas.

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