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Find out how long it takes a $2900 investment to double if it is invested at 8% compounded nt + monthly. Round to the nearest tenth of a year. Use the formula A =

A) 8.5 years
B) 8.9 years
C) 8.7 years
D) 9.1 years

User Sabobin
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Final answer:

An investment of $2900 at an 8% interest rate compounded monthly will take approximately 8.7 years to double. This is calculated using the compound interest formula and solving for the time variable t using natural logarithms.

Step-by-step explanation:

To find out how long it takes for a $2900 investment to double at an 8% interest rate compounded monthly, we use the formula for compound interest A = P(1 + r/n)^(nt), where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time the money is invested for, in years.

Since we want to double our principal, A = 2P.

Thus, our equation would be 2P = P(1 + r/n)^(nt), which simplifies to 2 = (1 + r/n)^(nt).

We can use logarithms to solve for t.

Given: P = $2900, r = 0.08 (8%), n = 12 (monthly compounding)

We need to solve the equation 2 = (1 + 0.08/12)^(12t).

Taking the natural logarithm of both sides gives us ln(2) = 12t * ln(1 + 0.08/12).

Therefore, t = ln(2) / (12 * ln(1 + 0.08/12)).

Calculating this gives us a t value of approximately 8.661, which rounded to the nearest tenth is 8.7 years. So, the correct answer is 8.7 years.

User Jkap
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