The simple interest formula is as follows:
[tex]I=P\cdot r\cdot t[/tex]Where P is the principal amount (the initial amount), r is the annual rate and t is the time in years.
The final amount is the initial amount plus the interest, so:
[tex]\begin{gathered} V=P+I \\ V=P+P\cdot r\cdot t \\ V=P(1+rt) \end{gathered}[/tex]We have the princiapl value $134,000, the final value $1,000,000 and the rate of 7.7%, so:
[tex]\begin{gathered} V=1000000 \\ P=134000 \\ r=7.7\%=0.077 \end{gathered}[/tex]So, we can solve for t and input the values:
[tex]\begin{gathered} V=P(1+rt) \\ \frac{V}{P_{}}=1+rt \\ rt=\frac{V}{P}-1 \\ t=\frac{\frac{V}{P}-1}{r} \end{gathered}[/tex][tex]\begin{gathered} t=\frac{\frac{1000000}{134000}-1}{0.077} \\ t=\frac{7.4626\ldots-1}{0.077} \\ t=\frac{6.4626\ldots}{0.077} \\ t=83.93\ldots\approx84 \end{gathered}[/tex]So, you must wait approximately 84 years.
