Approximately how many years would it take money to grow from $5,000 to $10,000 if it could earn 6% - brainly.com (2024)

To determine approximately how many years it would take for money to grow from $5,000 to $10,000 with a 6% interest rate, we can use the formula for compound interest.The formula for compound interest is:A = P(1 + r/n)^(nt)Where:A = the final amount of moneyP = the initial principal (starting amount)r = the interest rate (expressed as a decimal)n = the number of times interest is compounded per yeart = the number of yearsIn this case, the initial principal (P) is $5,000, the interest rate (r) is 6% (or 0.06 as a decimal), and we want to find the number of years (t).Let's plug in the given values and solve for t:$10,000 = $5,000(1 + 0.06/n)^(nt)To simplify the equation, let's assume that the interest is compounded annually (n = 1):$10,000 = $5,000(1 + 0.06)^(1t)Now we can solve for t by isolating it:(1 + 0.06)^t = $10,000/$5,000(1.06)^t = 2To find the value of t, we need to take the logarithm of both sides of the equation. Let's use the natural logarithm (ln) here:ln[(1.06)^t] = ln(2)Using the property of logarithms, we can bring the exponent down:t ln(1.06) = ln(2)Now we can solve for t by dividing both sides of the equation by ln(1.06):t = ln(2)/ln(1.06)Using a calculator, we can find that ln(2) ≈ 0.6931 and ln(1.06) ≈ 0.0583. Dividing these values gives us:t ≈ 0.6931/0.0583 ≈ 11.9So, approximately, it would take around 11.9 years for the money to grow from $5,000 to $10,000 with a 6% interest rate.