What will be the amount in an account with initial principal $6000 if interest is compounded continuously at an annual rate of 3.25% for 9 years?
amount= 6000(e^(.0325(9)) = 8038.64
8038.64
To calculate the final amount in the account with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = Final amount
P = Initial principal
e = Euler's number (approximately 2.71828)
r = Annual interest rate (as a decimal)
t = Number of years
Given:
P = $6000
r = 3.25% = 0.0325 (as a decimal)
t = 9 years
Plugging in the values, the formula becomes:
A = 6000 * e^(0.0325 * 9)
Calculating the exponential part:
e^(0.0325 * 9) ≈ 1.29128
Multiplying the initial principal by the exponential part:
A = 6000 * 1.29128
A ≈ $7,747.68
Therefore, the amount in the account after 9 years with continuous compounding will be approximately $7,747.68.
To calculate the amount in an account with continuously compounded interest, we can use the formula:
A = P * e^(rt)
Where:
A is the final amount in the account
P is the initial principal
e is Euler's number (approximately 2.71828)
r is the interest rate
t is the time in years
In this case, we have:
P = $6000
r = 3.25% (or 0.0325 as a decimal)
t = 9 years
Plugging the values into the formula, we get:
A = 6000 * e^(0.0325 * 9)
To evaluate this expression, you can use a calculator that has the exponentiation and Euler's number functions. After performing the calculation, the resulting value will be the final amount in the account after 9 years of continuously compounded interest.