Final answer:
To find the years it would take for a debt of $25,426 to grow to $47,857 at a 3.9% compound interest rate, we use the compound interest formula and solve for time, assuming interest is compounded annually.
Step-by-step explanation:
The student's question pertains to the time it will take for a debt to grow to a certain amount with a given compound interest rate. To answer this question, we use the compound interest 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 (in decimal form).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
Assuming the interest is compounded once a year (n=1), we can set up the equation: 47,857 = 25,426(1 + 0.039)^t.
To find t, we rearrange the formula to solve for t, which is done by taking the natural logarithm (ln) of both sides:
t = ln(47,857 / 25,426) / ln(1.039)
After calculating, we find the value of t, which is the number of years required for the debt to grow to $47,857.