a saving account with an initial balance of $15000 grows at 1.33percent per year compounded continuously. How much will the saving account have after 30 years?
15000 * e^(30*0.0133)
To find out how much the saving account will have after 30 years, we can use the formula for continuous compounding:
A = P * e^(rt)
Where:
A = the final amount after time t
P = the initial balance or principal
e = the base of the natural logarithm (approximately 2.71828)
r = the interest rate per year (expressed as a decimal)
t = the time period in years
Given:
P = $15,000
r = 1.33% = 0.0133 (expressed as a decimal)
t = 30 years
First, let's calculate the value of e^(rt):
e^(rt) = e^(0.0133 * 30)
e^(rt) ≈ 2.71828^(0.0133 * 30)
e^(rt) ≈ 2.71828^(0.399)
Now, we can calculate the final amount A:
A = P * e^(rt)
A = $15,000 * 2.71828^(0.399)
Using a calculator, we evaluate 2.71828^(0.399) and multiply it by $15,000 to find the final amount A.
After 30 years, the saving account will have approximately $25913.35.