Final answer:
Neville's $5,000 investment will grow in 30 years at a 5.5% interest rate using the compound interest formula A = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on the topic of compound interest. To calculate how much Neville's $5,000 investment will grow to in 30 years at a 5.5% annual interest rate, we will use 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.
- t is the time the money is invested for, in years.
Since the question does not specify how often the interest is compounded, we'll assume it is compounded annually (n = 1).
Therefore, A = $5,000(1 + 0.055/1)^(1*30) = $5,000(1 + 0.055)^30
Now, we calculate:
A = $5,000 * (1.055)^30
To find the value of A, simply calculate the above expression, which will give you the total value of the account after 30 years.