how would you write an equaton if you deposit $3200 into an account that earns 6.2% interest, compounded continuously?
general formula for continuous growth, were r is the rate of growth and t is time
amount = initialvalue (e^(rt))
so
amount = 3200 e^.062t
thanks
To write an equation that models the scenario of depositing $3200 into an account earning 6.2% interest compounded continuously, we can use the formula for continuous compound interest:
A = P * e^(rt)
where:
A = the final amount (including the interest)
P = the principal amount (initial deposit)
e = Euler's number, approximately 2.71828
r = annual interest rate (expressed as a decimal)
t = time (in years)
In this case, P = $3200, r = 6.2% = 0.062 (converted to decimal), and we're assuming an unknown time t.
The equation becomes:
A = 3200 * e^(0.062t)
This equation will allow us to calculate the final amount A given any desired time t.