Final answer:
To calculate the value of two investments with different interest rates and compounding periods after 10 years, we use the compound interest formula. The first bank's investment, compounded annually, would result in approximately $1628.89, while the second bank's, compounded quarterly, would result in approximately $1614.47. The difference is about $14, rounded to the nearest dollar.
Step-by-step explanation:
To find the difference between the values of two investments after 10 years, each with different compounding periods, we need to apply 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, and t is the time the money is invested for in years.
First Bank Investment
For the first bank offering 5% interest compounded annually, the calculation is:
A1 = 1000(1 + 0.05/1)^(1*10) = 1000(1.05)^10 ≈ $1628.89
Second Bank Investment
For the second bank offering 4.95% interest compounded quarterly, the calculation is:
A2 = 1000(1 + 0.0495/4)^(4*10) = 1000(1.012375)^40 ≈ $1614.47
The difference in value after 10 years between the two investments, rounded to the nearest dollar, is:
Difference = A1 - A2 ≈ $1628.89 - $1614.47 ≈ $14