Suppose you invest $2500 at an annual interest rate of 3% compounded continuously. How much will you have in the account after 7 years? Round the solution to the nearest dollar
Exact Form 25000e^0.2
answer: $3084
2500*e^(.03*7) = ?
D .. 3084
3084
Tia invests $2,500 at an interest rate of 4%, compounded quarterly. How much is the investment worth at the end of 5 years
2,500 is invested at an annual interest rate of 3% how much would it be after 10 years
To calculate the amount in the account after 7 years with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the amount in the account after t years
P = the principal amount (initial investment)
e = Euler's number (approximately equal to 2.71828)
r = the annual interest rate (as a decimal)
t = the number of years
In this case:
P = $2500
r = 3% = 0.03 (as a decimal)
t = 7 years
First, let's calculate e^(rt):
e^(rt) = e^(0.03 * 7)
To evaluate this expression, we need to find the value of e^(0.03 * 7). Mathematically, the power can be simplified as:
e^(0.03 * 7) = e^(0.21)
Now, using a scientific calculator or an online calculator, we can determine that e^(0.21) is approximately equal to 1.232339.
Next, we substitute the values into the formula:
A = $2500 * 1.232339
Multiplying these values, we find:
A ≈ $3080.85
Therefore, you will have approximately $3080.85 in the account after 7 years. Rounded to the nearest dollar, the answer is $3081.