Answer:
We can use the continuous compounding formula to solve this problem:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.
In this problem, we know the final amount (A = $1255.66), the interest rate (r = 4% = 0.04), and the time (t = 4 years). We want to find the initial amount (P).
Substituting the known values into the formula, we get:
1255.66 = Pe^(0.04*4)
Simplifying the exponent:
1255.66 = Pe^0.16
Dividing both sides by e^0.16:
1255.66 / e^0.16 = P
Using a calculator to evaluate e^0.16, we get:
1255.66 / 1.17351087099 = P
Simplifying:
P = $1069.44
Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).
Explanation:
compounded continuously, given that there is $1255.66 in the account after four years, we can use the formula:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.
Substituting the known values into the formula, we get:
1255.66 = Pe^(0.04*4)
Simplifying the exponent:
1255.66 = Pe^0.16
Dividing both sides by e^0.16:
P = 1255.66 / e^0.16
Using a calculator to evaluate e^0.16, we get:
P = 1069.44
Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).
rate 5 stars po if this helps u~ welcome po!