To calculate the total value of Martin's college fund after 18 years with an initial deposit (principal) of $5,000 and an annual compound interest rate of 7.3%, we can use the formula for compound interest:
\[ A = P(1 + r)^n \]
Where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = the principal amount (the initial amount of money).
- \(r\) = annual interest rate (decimal).
- \(n\) = number of years the money is invested or borrowed.
Given Values:
- \(P = 5000\)
- \(r = 0.073\) (7.3% as a decimal)
- \(n = 18\)
Step 1: Calculate the total value after 18 years
Plugging these values into the formula:
\[ A = 5000(1 + 0.073)^{18} \] \[ A = 5000(1.073)^{18} \]
Now, calculate \( (1.073)^{18} \):
\[ (1.073)^{18} \approx 3.588 \]
Now, multiply by the principal:
\[ A \approx 5000 \times 3.588 \approx 17940 \]
Final Amount
Thus, the total value of the account after 18 years is approximately:
\[ A \approx 17940.20 \]
Step 2: Calculate the interest earned
To find the interest earned, subtract the principal from the total amount:
\[ \text{Interest} = A - P = 17940.20 - 5000 \] \[ \text{Interest} \approx 12940.20 \]
Summary
- The final amount of the college fund is $17,940.20.
- The amount of interest earned on the account is $12,940.20.
Final Answers:
- Final Amount: $17,940.20
- Interest Earned: $12,940.20