To solve this problem, we'll use the formula for compound interest which is A = P(1 + r/n)^(nt). Here,
- 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 (in decimal form - e.g., 8% = 0.08).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Using the given values in the question,
- We have P = $4500 as the initial amount.
- The annual interest rate r = 8% = 0.08 (after dividing by 100 to convert percentage into a decimal).
- The interest is compounded monthly, hence the value for n is twelve, n = 12.
- The time t = 8 years.
Substituting the given values into the compound interest formula gives us
A = 4500 * (1 + 0.08/12)^(12*8)
After performing the calculation, the final amount A comes out to be approximately $8516.06.
Hence, the amount in the account after 8 years is around $8516.06.