Final answer:
To triple in value, the deposit will take approximately 6.31 years, while a 34% increase will take approximately 1.47 years.
Step-by-step explanation:
To determine how soon the deposit will triple in value, we can use the formula for compound interest: A = P * e^(rt), where A is the final amount, P is the initial deposit, r is the interest rate, and t is the time in years.
(A) Triple value:
Let P be the initial deposit, and A be the final amount. We want A to be three times P. Plugging in the values, we get: 3P = P * e^(0.11t) ⇒ 3 = e^(0.11t) ⇒ ln(3) = 0.11t ⇒ t = ln(3) / 0.11 ≈ 6.31 years.
(B) 34% increase:
To find the time it takes for the deposit to increase by 34%, we can use the formula: A = P * e^(rt). Plugging in the values, we get: (1 + 0.34)P = P * e^(0.11t) ⇒ 1.34 = e^(0.11t) ⇒ t = ln(1.34) / 0.11 ≈ 1.47 years.