5800 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 27500 dollars? Answer:

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5800 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 27500 dollars? Answer:

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Identify type of interest: Identify the type of interest being applied. Since the problem does not specify compound or simple interest, we will assume compound interest is being applied, which is common for savings accounts.Determine compound interest formula: Determine the formula to use for compound interest. The compound interest formula 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.Convert rate to decimal: Convert the annual interest rate from a percentage to a decimal. 6.25% as a decimal is 0.0625.Assume annual compounding: Assume that the interest is compounded once per year (n=1) for simplicity, as the problem does not specify.Set up and solve equation: Set up the equation with the given values and solve for t. A = 27500, P = 5800, r = 0.0625, n = 1. 27500 = 5800(1 + 0.0625/1)^(1*t)Simplify and solve for t: Simplify the equation and solve for t. 27500 = 5800(1 + 0.0625)^t 27500/5800 = (1.0625)^t 4.74137931034 ≈ (1.0625)^tUse logarithms to solve: Use logarithms to solve for t. Take the natural logarithm (ln) of both sides to get: ln(4.74137931034) ≈ t * ln(1.0625)Calculate natural logarithm: Calculate the natural logarithm of both sides. ln(4.74137931034) ≈ t * ln(1.0625) t ≈ ln(4.74137931034) / ln(1.0625)Perform calculations: Perform the calculations. t ≈ ln(4.74137931034) / ln(1.0625) t ≈ 1.55603762015 / 0.060624621 t ≈ 25.6666666667Round result to nearest year: Round the result to the nearest year. t ≈ 26 years

$5800$ 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 $27500$ dollars? $\newline$ Answer:

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580058005800 dollars is placed in an account with an annual interest rate of 6.25% 6.25 \% 6.25%. To the nearest year, how long will it take for the account value to reach 275002750027500 dollars?\newlineAnswer:

$5800$ 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 $27500$ dollars? $\newline$ Answer: