Problema Solution
If 5000 dollars is invested in a bank account at an interest rate of 10 per cent per year, compounded continuously. How many years will it take for your balance to reach 40000 dollars?
NOTE: Give your answer to the nearest tenth of a year.
Answer provided by our tutors
P = $5,000 the money invested
r = 0.10 that is 10% annual interest rate
A = $40,000 the future or maturity value after t years
e = 2.718281828 is Napier's constant
t = ? number of years we need to find
A = P*e^(r*t)
40000 = 5000*e^(0.1t)
e^(0.1t) = 40000/5000
e^(0.1t) = 8
e^(0.1t) = 2^3 use ln on both sides
0.1t = 3ln2
t = 0.1*3ln2
t = 30*ln2
t = 20.8 years to the nearest tenth
it will take 20.8 years for the balance to reach $40,000.