Question

Find the time (in years) for the investment to double. (Round your answer to two decimal places)

Answer 1

Step 1

Write the compound interest formula

`\text{A = P\lparen1 + }(r)/(n))^(nt)`

Step 2

n = 4 (quarterly)

`\begin{gathered} \text{P = x} \\ \text{A = 2x} \\ r\text{ = 7}(3)/(4)\text{ = 7.75\% = 0.0775} \end{gathered}`

Step 3:

Substitute in the formula to find t.

`\begin{gathered} 2x\text{ = x\lparen 1 + }(0.0775)/(4))^(4t) \\ \text{2 = \lparen1 + 0.019375\rparen}^4t \\ \text{2 = 1.019375}^(4t) \\ Take\text{ natural logarithm of both sides} \\ In(2)\text{ = 4t In\lparen1.019375\rparen} \\ 4t\text{ = }(ln(2))/(ln(1.019375)) \\ 4t\text{ = 36.12080351} \\ t\text{ = }(36.12080351)/(4) \\ t\text{ = 9.03 years} \end{gathered}`

Final answer

t = 9.03