Question

Find the total balance of each investment account earning simple annual interest.

A: $624 at 5% for 3 years
$624
B: $4,120 at 7% for 18 months
C: $900 at 3.1% for 6 months
D: $275 at 4.8% for 8 years

Answer 1

To find the total balance of each investment account earning simple annual interest, we can use the formula for simple interest:

\[
\text{Total Balance} = P + I
\]

where \( P \) is the principal (initial amount), and \( I \) is the interest earned, which can be calculated using the formula:

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

where:
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time in years.

Let's compute the total balance for each account.

**A: $624 at 5% for 3 years**

1. Calculate the interest:
\[
I = 624 \times 0.05 \times 3 = 624 \times 0.15 = 93.6
\]
2. Calculate the total balance:
\[
\text{Total Balance} = 624 + 93.6 = 717.6
\]

**B: $4,120 at 7% for 18 months**

First, convert 18 months into years:
\[
t = \frac{18}{12} = 1.5 \text{ years}
\]

1. Calculate the interest:
\[
I = 4120 \times 0.07 \times 1.5 = 4120 \times 0.105 = 433.6
\]
2. Calculate the total balance:
\[
\text{Total Balance} = 4120 + 433.6 = 4553.6
\]

**C: $900 at 3.1% for 6 months**

Convert 6 months into years:
\[
t = \frac{6}{12} = 0.5 \text{ years}
\]

1. Calculate the interest:
\[
I = 900 \times 0.031 \times 0.5 = 900 \times 0.0155 = 13.95
\]
2. Calculate the total balance:
\[
\text{Total Balance} = 900 + 13.95 = 913.95
\]

**D: $275 at 4.8% for 8 years**

1. Calculate the interest:
\[
I = 275 \times 0.048 \times 8 = 275 \times 0.384 = 105.6
\]
2. Calculate the total balance:
\[
\text{Total Balance} = 275 + 105.6 = 380.6
\]

Now, summarizing the results:

- **A: Total Balance = $717.60**
- **B: Total Balance = $4,553.60**
- **C: Total Balance = $913.95**
- **D: Total Balance = $380.60**