Final answer:
To calculate how many years it would take for a debt to grow by 35% with an annual compound interest rate of 5.7% and 107 compoundings per year, we can use the compound interest formula. Solving for t using the given values, we find that it would take approximately 1.5 months for the debt to grow by 35%.
Step-by-step explanation:
To calculate how many years it would take for a debt to grow by 35% with an annual compound interest rate of 5.7% and 107 compoundings per year, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we want to find t. Let's plug in the values we have: A = P(1 + 0.057/107)^(107t).
Since we know that the debt grows by 35%, the final amount (A) will be 1.35 times the initial amount (P): 1.35P = P(1 + 0.057/107)^(107t).
Now we can solve for t. Divide both sides of the equation by P and take the natural logarithm (ln) of both sides: ln(1.35) = (0.057/107)^(107t).
Finally, divide both sides of the equation by (0.057/107)^(107t) and solve for t using a calculator: t = ln(1.35) / ln(1 + 0.057/107) = 0.1254.
Therefore, it would take approximately 0.1254 years, or 1.5 months, for the debt to grow by 35%.