To calculate how much John will have in his account after 7 months at a yearly simple interest rate of 3.25%, we use the formula for simple interest:
[tex]\[ I = P \cdot r \cdot t \][/tex]
where:
- [tex]\( I \)[/tex] is the interest earned,
- [tex]\( P \)[/tex] is the principal amount (initial amount deposited),
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( t \)[/tex] is the time the money is invested or borrowed for, in years.
Here's how you perform the calculation step by step:
1. Determine the Principal (P):
The principal, [tex]\( P \)[/tex], is the initial amount deposited, which is [tex]$2000.
2. Convert the Annual Interest Rate to a Decimal (r):
The annual interest rate is 3.25%. To convert this percentage into a decimal, you divide by 100:
\[ r = \frac{3.25}{100} = 0.0325 \]
3. Convert the Time to Years (t):
John’s money will be invested for 7 months. Since the interest rate is annual, you need to express the time in years. There are 12 months in a year, so the time in years is:
\[ t = \frac{7}{12} \text{ years} \]
4. Calculate the Interest Earned (I):
Now, plug in the values into the formula for simple interest:
\[ I = P \cdot r \cdot t \]
\[ I = 2000 \cdot 0.0325 \cdot \frac{7}{12} \]
5. Calculate the Interest Numerically:
\[ I = 2000 \cdot 0.0325 \cdot 0.5833... \]
\[ I \approx 2000 \cdot 0.0189583 \]
\[ I \approx 37.92 \]
So the interest earned after 7 months is approximately $[/tex]37.92.
6. Determine the Total Amount in the Account:
Now, add the interest earned to the principal to find out the total amount in the account after 7 months:
[tex]\[ \text{Total amount} = P + I \][/tex]
[tex]\[ \text{Total amount} = 2000 + 37.92 \][/tex]
[tex]\[ \text{Total amount} \approx 2037.92 \][/tex]
So, after 7 months, John will have approximately $2037.92 in his account.
