Final answer:
By applying the compound interest formula and plugging in the provided values, we find that Tanisha will need approximately 6.5 years for her investment to grow from $100 to $150 at an 8% annual interest rate compounded monthly.
Step-by-step explanation:
To determine how long it will take for Tanisha's $100 investment at an 8% annual interest rate compounded monthly to grow to $150, we can use the compound interest formula: A = P(1 + r/n)^(nt). Here, A is the amount of money accumulated after n years, including interest, P is the principal amount ($100), r is the annual interest rate (8% or 0.08), n is the number of times that interest is compounded per year (12 for monthly), and t is the number of years.
From the information provided, we know that after three years the total is $115.76 due to compound interest, so let's solve for t when A is $150:
- A = $150
- P = $100
- r = 0.08
- n = 12
We can now rearrange the formula to solve for t:
t = ln(A/P) / (n * ln(1 + r/n))
Plugging in the values we get:
t = ln(150/100) / (12 * ln(1 + 0.08/12))
t ≈ 6.116
Since this value is closest to option a), approximately 6.5 years, Tanisha will need roughly 6.5 years for her $100 investment to grow to $150 with the given compound interest conditions.