If you put $2,000 in a savings account that pays 6% interest compounded continuously, how much money will you have in your account in 4 years? Assume you make no additional deposits or withdrawals
2,000 e^.06 t
2,000 e^.24
2,000 * 1.27124915
$ 2,542.50
thanks Damon :)
How long will it take $8000 to grow to $20,000 if the rate of interest is 7% compounded continuously?
To calculate the amount of money you will have in your savings account after 4 years with continuously compounded interest, you can use the formula:
A = P * e^(rt)
Where:
A is the final amount (the balance) in your account after 4 years
P is the principal amount (the initial deposit) of $2,000
e is the mathematical constant approximately equal to 2.71828
r is the interest rate (6% or 0.06)
t is the time period in years (4)
To get the answer, let's plug these values into the formula:
A = $2,000 * e^(0.06*4)
Now, let's calculate it step by step.
1. Calculate the exponential part: e^(0.06*4)
- Multiply the interest rate (0.06) by the time period (4)
- 0.06 * 4 = 0.24
- e^(0.24) ≈ 1.2712491 (using a calculator)
2. Multiply the result by the principal amount:
- A = $2,000 * 1.2712491
- A ≈ $2,542.4982
Therefore, after 4 years, you will have approximately $2,542.50 in your savings account.