7600 dollars is placed in an account with an annual interest rate of 6.25%. To the nearest year, how long will it take for the account value to reach 16000 dollars? Answer:

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7600 dollars is placed in an account with an annual interest rate of  6.25%. To the nearest year, how long will it take for the account value to reach 16000 dollars? Answer:

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Identify Formula: Identify the formula to use for compound interest. The formula for compound interest is A = P(1 + r/n)^(nt), where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money). r = the annual interest rate (decimal). n = the number of times that interest is compounded per year. t = the time the money is invested for, in years. Since the problem does not specify how often the interest is compounded, we will assume it is compounded annually, so n = 1.Set Up Equation: Set up the equation with the given values and solve for t. We have P = $7600, A = $16000, r = 6.25% or 0.0625, and n = 1. The equation becomes $16000 = $7600(1 + 0.0625/1)^(1*t).Simplify and Isolate: Simplify the equation and isolate the exponential part. $16000 = $7600(1 + 0.0625)^(t) $16000 = $7600(1.0625)^(t) To isolate t, we need to divide both sides by $7600. $16000 / $7600 = (1.0625)^(t)Calculate Left Side: Calculate the left side of the equation. $16000 / $7600 = 2.10526315789 (approximately) So, 2.10526315789 = (1.0625)^(t)Take Natural Logarithm: Take the natural logarithm of both sides to solve for t. ln(2.10526315789) = ln((1.0625)^(t)) Use the property of logarithms that ln(a^b) = b*ln(a). ln(2.10526315789) = t * ln(1.0625)Calculate Logarithm: Calculate the natural logarithm of both sides. ln(2.10526315789) ≈ 0.7447274949 ln(1.0625) ≈ 0.06062462182 Now, divide the logarithm of the left side by the logarithm of the right side to find t. t = ln(2.10526315789) / ln(1.0625) t ≈ 0.7447274949 / 0.06062462182Calculate Value: Calculate the value of t. t ≈ 0.7447274949 / 0.06062462182 t ≈ 12.28 Since we need to find the nearest year, we round t to the nearest whole number. t ≈ 12 years

$7600$ dollars is placed in an account with an annual interest rate of $6.25 \%$ . To the nearest year, how long will it take for the account value to reach $16000$ dollars? $\newline$ Answer:

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$7600$ dollars is placed in an account with an annual interest rate of $6.25 \%$ . To the nearest year, how long will it take for the account value to reach $16000$ dollars? $\newline$ Answer: