Final answer:
Sam will have approximately $57.88 in his account after 3 years with 5% compound interest compounded annually on his initial $50.
Step-by-step explanation:
The question is asking us to calculate the future value of $50 with 5% compound interest compounded annually over 3 years. To find out the amount Sam will have after 3 years, we can use the compound interest formula: 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 sum of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In Sam's case, P = $50, r = 0.05 (5%), n=1 (since it is compounded annually), and t = 3 years. Plugging in these values,
the formula becomes:
A = $50(1 + 0.05/1)^(1*3)
This simplifies to:
A = $50(1.05)^3
After calculation, we find that the total future amount that Sam will have after 3 years to the nearest cent is approximately:
A = $50(1.157625) = $57.88