48 weeks ago, Gabriella invested at 3.9% interest, compounded weekly. Today, her investment is worth $225.50. How much interest has Gabriella's account earned in the past 48 weeks?
P(1+.039/52)^(48) = 225.50
P = 217.59
225.50-217.59 = 7.91 interest
Thanks Steve!!!
To find out the amount of interest Gabriella's account has earned in the past 48 weeks, we need to follow these steps:
Step 1: Determine the initial amount invested.
In this case, the initial amount invested is unknown. Let's denote it as 'P'.
Step 2: Determine the interest rate.
Gabriella invested at 3.9% interest, compounded weekly. In decimal form, this would be 0.039.
Step 3: Determine the time period.
The time period is 48 weeks.
Step 4: Use the compound interest formula to calculate the future value.
The compound interest formula is given by: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
In this case, we know the future value (A) is $225.50, the interest rate (r) is 0.039, and the time (t) is 48 weeks. Since the interest is compounded weekly, n = 52 (the number of weeks in a year).
So the formula becomes: $225.50 = P(1 + 0.039/52)^(52/48).
Step 5: Solve for the principal amount (P).
Divide both sides of the equation by (1 + 0.039/52)^(52/48) to isolate P.
P = $225.50 / (1 + 0.039/52)^(52/48).
Using a calculator, evaluate the expression to find the value of P.
Step 6: Find the interest earned.
To find the interest earned, subtract the initial amount invested (P) from the final amount (A).
Interest = A - P.
Using the values you found, you can calculate the interest Gabriella's account has earned in the past 48 weeks.