Questions: Questão 5: Uma enfermeira investiu R 5.000 a uma taxa de juros simples de 6% ao ano. Quanto tempo levará para o montante atingir R 6.800? (a) 4 anos (b) 5 anos (c) 6 anos (d) 7 anos (e) 8 anos

Solution Steps

To solve this problem, we need to use the formula for simple interest:

\[ A = P(1 + rt) \]

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 (in decimal).
• \( t \) is the time the money is invested for in years.

We need to solve for \( t \) when \( A = 6800 \), \( P = 5000 \), and \( r = 0.06 \).

1. Rearrange the simple interest formula to solve for \( t \).
2. Substitute the given values into the formula.
3. Calculate the value of \( t \).

Para encontrar o tempo \( t \), começamos com a fórmula de juros simples:

\[ A = P(1 + rt) \]

Rearranjamos a fórmula para resolver \( t \):

\[ t = \frac{A}{P} - 1 \]

Substituímos os valores fornecidos na fórmula:

\[ P = 5000 \] \[ A = 6800 \] \[ r = 0.06 \]

\[ t = \frac{6800}{5000} - 1 \]

Calculamos o valor de \( t \):

\[ t = \frac{6800}{5000} - 1 \] \[ t = 1.36 - 1 \] \[ t = 0.36 \]

Finalmente, dividimos por \( r \):

\[ t = \frac{0.36}{0.06} \] \[ t = 6 \]

Final Answer