Pergunta

Suppose Debra places 4000 in an account that pays 12% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. square (b) Find the amount in the account at the end of 2 years. square
Solução

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AlexandroMestre · Tutor por 5 anos
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(a) To find the amount in the account at the end of 1 year, we can use the formula for compound interest:<br /><br />\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]<br /><br />where:<br />- \( A \) is the amount in the account after \( t \) years,<br />- \( P \) is the principal amount (initial amount),<br />- \( r \) is the annual interest rate (in decimal form),<br />- \( n \) is the number of times interest is compounded per year,<br />- \( t \) is the time the money is invested for in years.<br /><br />In this case, the interest is compounded annually, so \( n = 1 \).<br /><br />Given:<br />- \( P = \$4000 \)<br />- \( r = 12\% = 0.12 \)<br />- \( n = 1 \)<br />- \( t = 1 \) year<br /><br />Substitute these values into the formula:<br /><br />\[ A = 4000 \left(1 + \frac{0.12}{1}\right)^{1 \cdot 1} \]<br />\[ A = 4000 \left(1 + 0.12\right)^1 \]<br />\[ A = 4000 \cdot 1.12 \]<br />\[ A = 4480 \]<br /><br />So, the amount in the account at the end of 1 year is \$4480.<br /><br />(b) To find the amount in the account at the end of 2 years, we use the same formula but change \( t \) to 2:<br /><br />\[ A = 4000 \left(1 + \frac{0.12}{1}\right)^{1 \cdot 2} \]<br />\[ A = 4000 \left(1 + 0.12\right)^2 \]<br />\[ A = 4000 \cdot 1.12^2 \]<br />\[ A = 4000 \cdot 1.2544 \]<br />\[ A = 5017.60 \]<br /><br />So, the amount in the account at the end of 2 years is \$5017.60.
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