200000=P ×(1+(13)/(100))^(10)

Set up compound interest formula: To solve for the initial principal P, we need to rearrange the compound interest formula to solve for P. The formula is given by A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this problem, A = 200,000, r = 13/100 = 0.13, n = 1 (since the interest is compounded annually), and t = 10 years.Plug in given values: First, we plug in the given values into the formula: 200,000 = P × (1 + 0.13)^(10).Simplify expression: Next, we simplify the expression inside the parentheses: 1 + 0.13 = 1.13.Calculate value: Now, we raise 1.13 to the power of 10: (1.13)^(10). Using a calculator, we find that (1.13)^(10) ≈ 3.39357057.Divide both sides: We then divide both sides of the equation by 3.39357057 to solve for P: P = 200,000 / 3.39357057.Perform division: Finally, we perform the division: P ≈ 200,000 / 3.39357057 ≈ 58,946.12.

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$200000=P \times\left(1+\frac{13}{100}\right)^{10}$

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Algebra 2

Sum of finite series starts from 1

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200000=P \times\left(1+\frac{13}{100}\right)^{10}

Set up compound interest formula: To solve for the initial principal $P$ , we need to rearrange the compound interest formula to solve for $P$ . The formula is given by $A = P(1 + r/n)^{(nt)}$ , where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. In this problem, $A = 200,000$ , $P$ $0$ , $P$ $1$ (since the interest is compounded annually), and $P$ $2$ years.
Plug in given values: First, we plug in the given values into the formula: $200,000 = P \times (1 + 0.13)^{10}$ .
Simplify expression: Next, we simplify the expression inside the parentheses: $1 + 0.13 = 1.13$ .
Calculate value: Now, we raise $1.13$ to the power of $10$ : $(1.13)^{10}$ . Using a calculator, we find that $(1.13)^{10} \approx 3.39357057$ .
Divide both sides: We then divide both sides of the equation by $3.39357057$ to solve for $P$ : $P = \frac{200,000}{3.39357057}.$
Perform division: Finally, we perform the division: $P \approx \frac{200,000}{3.39357057} \approx 58,946.12$ .