Answer: To determine the time it would take to save $3400 in an account with a 0.12% interest rate compounded continuously to end up with $5000, we can use the continuous compound interest formula:
A = Pe^(rt)
Where:
A = the final amount in the account ($5000 in this case)
P = the initial amount in the account ($3400 in this case)
e = the mathematical constant e (approximately equal to 2.71828)
r = the annual interest rate (0.12% = 0.0012 as a decimal)
t = the time in years
We can rearrange this formula to solve for t:
t = ln(A/P) / r
Substituting the values given, we get:
t = ln(5000/3400) / 0.0012
t = 28.58 years (rounded to two decimal places)
Therefore, it would take approximately 28.58 years to save $3400 in an account with a 0.12% interest rate compounded continuously to end up with $5000.
Explanation: