Question

Your $440 you got from graduation is placed in a bank account that receives a 5.8% interest rate compounded annually. If you leave your money in the account for 8 years, how much will it be worth when you take it out?

Answer 1

Using the compound interest formula FV = P(1 + r)^n, $440 in a bank account at a 5.8% annual interest rate compounded annually will be worth approximately $689.00 after 8 years.

Step-by-step explanation:

The student's question is asking how much $440 will be worth after 8 years in a bank account that receives a 5.8% interest rate compounded annually.

To calculate the future value of money in the context of compound interest, we can use the formula FV = P(1 + r)^n, where FV is the future value, P is the principal amount, r is the annual interest rate, and n is the number of years the money is invested.

For this scenario:

• Principal (P): $440
• Annual interest rate (r): 5.8% or 0.058
• Number of years (n): 8
  

Using the formula:

FV = 440(1 + 0.058)^8

To calculate the value, follow these steps:

1. Calculate 1 + r: 1 + 0.058 = 1.058
2. Raise this to the power of n: (1.058)^8 = approximately 1.565917
3. Multiply the result by the principal: 440 * 1.565917 = approximately $689.00

After 8 years, the money will have grown to approximately $689.00.