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
- Calculate the interest: \[ I = 624 \times 0.05 \times 3 = 624 \times 0.15 = 93.6 \]
- 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: \[ t = \frac{18}{12} = 1.5 \text{ years} \]
- Calculate the interest: \[ I = 4120 \times 0.07 \times 1.5 = 4120 \times 0.105 = 433.6 \]
- 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: \[ t = \frac{6}{12} = 0.5 \text{ years} \]
- Calculate the interest: \[ I = 900 \times 0.031 \times 0.5 = 900 \times 0.0155 = 13.95 \]
- Calculate the total balance: \[ \text{Total Balance} = 900 + 13.95 = 913.95 \]
D: $275 at 4.8% for 8 years
- Calculate the interest: \[ I = 275 \times 0.048 \times 8 = 275 \times 0.384 = 105.6 \]
- 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
2 answers