Answer:
78. t=8.66yrs
79. r=23.10%
80. r=11.0975%
Step-by-step explanation:
78. Given the initial deposit is $1,000 and the 8% compounded continuously. The doubling time can be calculated using the formula;
[tex]A=Pe^{it}[/tex]
Given that A=2P, we substitute in the equation to solve for t:
[tex]A=Pe^{rt}\\\\2P=Pe^{rt}\\\\2=e^{0.08t}\\\\0.08t=\ In 2\\\\t=8.66\ years[/tex]
Hence, it takes 8.66 years for $1,000 to double in value.
79.
Given the initial deposit is $1,000 and the r% compounded continuously.
-The doubling rate can be calculated using the formula;
[tex]A=Pe^{rt}[/tex]
#We substitute our values in the equation to solve for r:
[tex]A=Pe^{rt}\\\\A=2P, t=3\\\\\therefore\\\\2P=Pe^{3r}\\\\2=e^{3r}\\\\r=\frac{In \ 2}{3}\\\\=0.23105\approx 23.10\%[/tex]
Hence, the deposit will double in 3 years at a rate of 23.10%
80.
Given the initial deposit is $30,000 and the future value is $2,540,689.
-Also, given t=40yrs, the rate of growth for continuous compounding is calculated as:
[tex]A=Pe^{rt}, \ \ \ r=r, t=40yrs\\\\2540689=30000e^{40r}\\\\\frac{2540689}{30000}=e^{40r}\\\\r=\frac{In \ (2540689/30000)}{40}\\\\\\=0.110975=11.0975\%[/tex]
Hence, the deposit will grow at a rate of approximately 11.0975%
