(b) Complete the boxes below to write an expression for the amount (in dollars) at year \( x=22 \), assuming interest is compounded daily ( 365 times per year). Do not round any values. You can enter arithmetic expressions (containing \( +,-, *, / \), or \( \wedge \) ) in any of these boxes. \( \qquad \) Number Number Number What is the value in year \( x=22 \) of an investment of \( \$ 3,900 \) dollars which pays \( 7.77 \% \) compounded daily? \$ \( \square \) Number (Round to the nearest 0.01 dollars)
Solución de inteligencia artificial de Upstudy
Responder
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Beyond the Answer
To calculate the amount at year \( x = 22 \) for an investment of \$3,900 at an interest rate of 7.77% compounded daily, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is invested for. In this case: - \( P = 3900 \) - \( r = 0.0777 \) - \( n = 365 \) - \( t = 22 \) Now, substituting in the values: \[ A = 3900 \left(1 + \frac{0.0777}{365}\right)^{365 \times 22} \] Calculating further: 1. Compute \( \frac{0.0777}{365} \). 2. Add 1 to the result. 3. Raise that result to the power of \( 365 \times 22 \). 4. Multiply by 3900 to find \( A \). After performing the calculations, rounding to the nearest cent: The final amount \( A \) is approximately \( \$ 26,903.77 \).
