Answer :
Given:
Initial Amount, P = $1000
Rate of interest, r = 8% = 0.08
Number of years, t = ?
Number of compounding period, n = 2
Required: Time required to double the initial amount.
Explanation:
The formula to find the compound amount is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Since, A is the double of initial amount, A = $2000
Substitute the given values into the formula.
[tex]\begin{gathered} 2000=1000(1+\frac{0.08}{2})^{2\cdot t} \\ 2=1.04^{2t} \end{gathered}[/tex]Take logarithm with base 1.04 on both sides.
[tex]\begin{gathered} \log_{1.04}2=\log_{1.04}(1.04^{2t}) \\ 2t=17.67 \\ t=8.835 \end{gathered}[/tex]Thus, 8.835 years required to double the initial deposit.
Final Answer: 8.835 years required to double the initial deposit.