Suppose you invest $10000 at 5.1% annual interest, compounded weekly. How long will it take to double your money? Round to the nearest year. (Hint this will be a whole number)

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Suppose you invest  $10000 at  5.1% annual interest, compounded weekly. How long will it take to double your money? Round to the nearest year. (Hint this will be a whole number)

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Identify formula for compound interest: Identify the formula to use for compound interest. The formula for compound interest is 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 (decimal). n is the number of times that interest is compounded per year. t is the time the money is invested for in years. We want to find t when A is double the principal P.Set up equation with given values: Set up the equation with the given values. We know that A = 2P (since we want to double the money), P = $10,000, r = 5.1% or 0.051 (as a decimal), and n = 52 (since interest is compounded weekly). So, the equation becomes 2P = P(1 + 0.051/52)^(52t).Simplify the equation: Simplify the equation. We can divide both sides by P to get 2 = (1 + 0.051/52)^(52t).Solve for t: Solve for t. To solve for t, we need to take the natural logarithm (ln) of both sides: ln(2) = ln((1 + 0.051/52)^(52t)). Using the power rule of logarithms, we get: ln(2) = 52t * ln(1 + 0.051/52).Isolate t: Isolate t. Divide both sides by 52 * ln(1 + 0.051/52) to get: t = ln(2) / (52 * ln(1 + 0.051/52)).Calculate value of t: Calculate the value of t. Using a calculator, we find: t ≈ ln(2) / (52 * ln(1 + 0.051/52)). t ≈ 0.69314718056 / (52 * ln(1.00098039216)). t ≈ 0.69314718056 / (52 * 0.00098019802). t ≈ 0.69314718056 / 0.05097029604. t ≈ 13.60546875.Round answer to nearest year: Round the answer to the nearest year. Since we are asked to round to the nearest year, t ≈ 14 years.

Suppose you invest $\$ 10000$ at $5.1 \%$ annual interest, compounded weekly. How long will it take to double your money? Round to the nearest year. (Hint this will be a whole number)

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Suppose you invest $10000 \$ 10000 $10000 at 5.1% 5.1 \% 5.1% annual interest, compounded weekly. How long will it take to double your money? Round to the nearest year. (Hint this will be a whole number)

Suppose you invest $\$ 10000$ at $5.1 \%$ annual interest, compounded weekly. How long will it take to double your money? Round to the nearest year. (Hint this will be a whole number)