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Investing $10,000 in a savings account at 5% annual interest compounded semiannually will result in approximately how much money after 10 years?Use the formula: A= P( 1 + r/m) ^nta) $15,000.00b) $16,386.95c) $16,288.95d) $13,448.89

User Phwt
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1 Answer

2 votes

To solve for the compound interest semiannually:


A\text{ = P(1+}(r)/(n))^(nt)
\begin{gathered} \text{ Principal = \$10,000} \\ \text{rate = 5\%} \\ time=\text{ 10years} \end{gathered}

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for Amount = A, semiannually means twice in a year, n= 2


\begin{gathered} A\text{ = P(1+}(r)/(n))^(nt) \\ A=\text{ \$10000 (1+}(0.05)/(2))^(2(10)) \\ A=10000(1+0.025)^(20)\text{ } \\ A=10000(1.025)^(20) \\ A=\text{ \$10000(1.6386)} \\ A\text{ = \$16386} \end{gathered}

Therefore the annual interest compounded semiannually = $16386.95

Hence the correct answer is Option B

User Tim Hobbs
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