Final answer:
To determine how long it will take for $1,400 to grow to $1,900 at 9% simple interest, we calculate the total interest earned and then solve for time using the simple interest formula. It will take approximately 4 years for the investment to reach the desired amount.
Step-by-step explanation:
To solve Lance Lopes's problem about how long it will take for $1,400 to amount to $1,900 at 9% simple interest, we will use the formula for simple interest: I = PRT, where I is the interest earned, P is the principal amount (initial amount), R is the rate of interest per year, and T is the time in years. In this case, we want to find T.
First, we calculate the total interest earned (I) by subtracting the initial amount (P) from the final amount: I = $1,900 - $1,400 = $500.
Now we plug the values we have into the simple interest formula:
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- I = PRT
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- $500 = $1,400 × 0.09 × T
Solving for T:
- T = $500 / ($1,400 × 0.09)
- T ≈ 4.0 years (rounded to one decimal place)
Therefore, it will take approximately 4 years for Lance's investment to grow from $1,400 to $1,900 at a 9% simple interest rate.