Final answer:
After 5 years, Jaxson's investment of $8,100 at a 4.8% interest rate compounded monthly will grow to approximately $10,272.35 when rounded to the nearest cent.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, we use the 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 amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In Jaxson's case, the principal P is $8,100, the annual interest rate r is 4.8%, or 0.048 when expressed as a decimal, interest is compounded monthly so n is 12, and the time t is 5 years.
Using the formula, we calculate:
A = 8100(1 + 0.048/12)^(12*5)
Calculating this out, A equals approximately:
A = 8100(1 + 0.004)^(60)
A = 8100(1.004)^60
A ≈ 8100 * 1.268241
A ≈ 10,272.35
Therefore, after 5 years, the money in Jaxson's account will be approximately $10,272.35, after rounding to the nearest cent.