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.