In how many years does capital achieve an amount equivalent to capital plus 23.5%? Use a nominal annual interest rate of 6.125% compounded monthly. Please clearly specify in your answer whether the calculated period is months or years. Use all decimals.

To find out in how many years capital achieves an amount equivalent to capital plus 23.5% when compounded monthly at a nominal annual interest rate of 6.125%, you can use the formula for compound interest: A = P(1 + r/n)^(nt) Where: A = the future amount P = the principal amount (initial capital) r = the nominal annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = the number of years In this case, P is the initial capital, and we want to find t when A is equal to 1.235 times P (capital plus 23.5%). So, we have: 1.235P = P(1 + 0.06125/12)^(12t) Now, let's solve for t: 1.235 = (1 + 0.06125/12)^(12t) To isolate t, take the natural logarithm (ln) of both sides: ln(1.235) = ln((1 + 0.06125/12)^(12t)) ln(1.235) = 12t * ln(1 + 0.06125/12) Now, divide both sides by 12 * ln(1 + 0.06125/12): t = ln(1.235) / (12 * ln(1 + 0.06125/12)) Using a calculator: t ≈ 3.45484 So, it will take approximately 3.45484 years for the capital to achieve an amount equivalent to capital plus 23.5% when compounded monthly at a nominal annual interest rate of 6.125%. This period is in years.