Answer:
$13,304
Step-by-step explanation:
-We use the compound interest function to determine the rate of growth.
-Given that the amount doubles in 13 years, the annual growth rate is calculated as:
[tex]A=P(1+i)^n\\\\2P=P(1+i)^n\\\\\therefore 2=(1+i)^{13}\\\\i=2^{1/13}-1=0.05477[/tex]
We now substitute this value of i in the compound interest formula equation to solve for future value:
[tex]A=P(1+i)^n\\\\\\=7400(1.05477)^{11}\\\\\\=13303.54[/tex]
[tex]\approx13304[/tex]
Hence, the future value to the nearest dollar is $13,304
*You can alternatively use the exponential growth function:
[tex]P_t=P_oe^{rt}\\\\2=e^{13r}\\\\r=\frac{In \ 2}{13}=0.05332\\\\\therefore P_{11}=7400e^{0.05332\times 11}\\\\=13303.14[/tex]
This is slightly off by just $1
