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A invested $1000 at compounded annual interestrate.at the end of 12 yrs, the total amount will be $4000.in how many yrs will the total amount be $8000?
A invested $1000 at compounded annual interest rate. At the end of 12 years, the total amount will be $4000. In how many years will the total amount be $8000?
Let me calculate it for you. To begin with, we can determine the interest rate per year, assuming the interest is compounded annually. Using the formula, A = P(1 + r/n)^(nt), where A is the total amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. We have A = $4000, P = $1000, n = 1, and t = 12 years, so 4000 = 1000(1 + r/1)^(1*12). Solving for r, we get r = 0.116 or 11.6%. Now we can use the same formula with A = $8000 and P = $1000 and solve for t. 8000 = 1000(1 + 0.116/1)^(1*t), which simplifies to 8 = (1 + 0.116)^t. Taking logarithms of both sides, we get t = log(8)/log(1.116) = 21.69 years (rounded to two decimal places).