One thousand dollars is deposited in a savings account at 6% interest compounded continously.
How many years are required for the balance in the account to reach $2500
CONTINUOUSLY: A=Pe^(rt)
(e=2.71828 18284 59045 23536…)
PERIODICALLY: A=P(1+r/n)^(nt)
P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year
Since it's compounded continuously, use Pert (The first formula).
To calculate the number of years required for the balance in the account to reach $2500, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount in the account ($2500)
P = the principal amount ($1000)
r = the annual interest rate (6% or 0.06 in decimal form)
t = the time in years
We need to solve for t. Rearranging the formula, we have:
t = ln(A/P) / (r)
First, let's calculate the natural logarithm of (A/P), which is ln(2500/1000) = ln(2.5) ≈ 0.9163.
Next, we divide ln(2.5) by 0.06:
t = 0.9163 / 0.06 ≈ 15.27
Therefore, it would take approximately 15.27 years for the balance in the account to reach $2500 if the interest is compounded continuously.