Final answer:
Using the formula for continuous compound interest, the amount in the account after 8 years, with a principal of $1200 at a 4.5% annual rate, would be approximately $1720, which is answer b).
Step-by-step explanation:
The subject of the student's schoolwork question is related to compound interest, specifically with the interest compounded continuously. To calculate the final amount A in the account after 8 years, the formula for continuous compounding is applied:
A = P * e^(rt)
Where:
- P is the principal amount ($1200),
- e is the base of the natural logarithm,
- r is the annual interest rate (4.5% or 0.045 as a decimal),
- t is the time in years (8 years).
Plugging in the values, we get:
A = 1200 * e^(0.045 * 8)
Calculating the exponential part using a calculator gives us the final amount in the account:
A ≈ 1200 * e^(0.36)
A ≈ 1200 * 1.4333
A ≈ 1720
After compounding continuously for 8 years at a 4.5% annual rate, the amount in the account will be approximately $1720, which makes option b) the correct answer.