Respuesta :
Answer:
We can use the compound interest formula to solve this problem:
A = P * (1 + R/n)^(n*t)
Where:
A = Final amount
P = Initial principal amount
R = Interest rate (as a decimal)
n = Number of compounding periods per year (usually 1 for annual compounding)
t = Time in years
We are given that:
A = 4.5P (amount is 4.5 times the initial principal)
P = Initial principal amount (unknown)
R = 0.14 (14% interest rate)
n = 1 (assuming annual compounding)
t = Unknown (what we need to solve for)
We can rewrite the equation to solve for t:
t = log(A/P) / (n * log(1 + R/n))
Plugging in the known values:
t = log(4.5) / (1 * log(1 + 0.14/1))
t ≈ 12.27 years
Therefore, it will take approximately 12.27 years for the amount of money to become 4.5 times the initial sum at a 14% annual interest rate with annual compounding.
