Investment Calculation: How Long to Double $2900 at 8% Compounded Monthly?
What is the time period required for a $2900 investment to double at an 8% interest rate compounded monthly?
Which of the following options represents the correct time frame?
A) 8.5 years
B) 8.9 years
C) 8.7 years
D) 9.1 years
Answer:
An investment of $2900 at an 8% interest rate compounded monthly will take approximately 8.7 years to double.
To determine the duration for a $2900 investment to double at an 8% interest rate compounded monthly, we utilize the compound interest formula. The formula A = P(1 + r/n)^(nt) is used, where:
A is the accumulated amount after n years, including interest.
P is the principal amount (initial investment).
r is the annual interest rate (in decimal form).
n is the number of times interest is compounded per year.
t is the duration the money is invested for, in years.
Since the goal is to double the principal amount, we have A = 2P. This leads to the equation 2P = P(1 + r/n)^(nt), which simplifies to 2 = (1 + r/n)^(nt). By applying logarithms, we can solve for t.
Given: P = $2900, r = 0.08 (8%), n = 12 (monthly compounding)
Solving the equation leads to t = ln(2) / (12 * ln(1 + 0.08/12)). Calculating this yields a t value of approximately 8.661, rounded to 8.7 years. Therefore, it will take around 8.7 years for the $2900 investment to double at an 8% interest rate compounded monthly.