Final answer:
The question asks to find the time it takes for a principal of $4000 to grow to a balance of $5000 at a 5% annual interest rate. Assuming annual compounding, the formula A = P(1 + r/n)^(nt) is used to solve for time (t) where A is the amount ($5000), P is the principal ($4000), and r is the interest rate (5% as a decimal, 0.05).
Step-by-step explanation:
The student is asking to find the time it takes for an investment with a principal of $4000 at a 5% interest rate to grow to a balance of $5000. This question involves understanding of simple interest or compound interest. Assuming the interest is compounded annually, the formula to use is:
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 sum 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 this case, we are solving for t when A is $5000, P is $4000, r is 0.05 (5% expressed as a decimal), and n is assumed to be 1 since the compounding frequency is not specified:
5000 = 4000(1 + 0.05/1)^(1*t)
Solving for t gives us the time required for the balance to grow to $5000.