Answer: 1,000,000,000,000,000,000,000,
Step-by-step explanation:
Answer:
FYAB gives a better deal.
Step-by-step explanation:
Compound interest:
![A = P(1 + \dfrac{r}{n})^{nt}](https://tex.z-dn.net/?f=%20A%20%3D%20P%281%20%2B%20%5Cdfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%20)
Continuously compounded interest:
![A = Pe^{rt}](https://tex.z-dn.net/?f=%20A%20%3D%20Pe%5E%7Brt%7D%20)
For the quarterly compounded interest, r = 0.25%, and n = 4.
![2P = P(1 + \dfrac{0.0025}{4})^{4t}](https://tex.z-dn.net/?f=%202P%20%3D%20P%281%20%2B%20%5Cdfrac%7B0.0025%7D%7B4%7D%29%5E%7B4t%7D%20)
![1.000625^{4t} = 2](https://tex.z-dn.net/?f=%201.000625%5E%7B4t%7D%20%3D%202%20)
![\log (1.000625^{4t}) = \log 2](https://tex.z-dn.net/?f=%20%5Clog%20%281.000625%5E%7B4t%7D%29%20%3D%20%5Clog%202%20)
![4t(\log 1.000625) = \log 2](https://tex.z-dn.net/?f=%204t%28%5Clog%201.000625%29%20%3D%20%5Clog%202%20)
![t = \dfrac{\log 2}{4\log 1.000625}](https://tex.z-dn.net/?f=%20t%20%3D%20%5Cdfrac%7B%5Clog%202%7D%7B4%5Clog%201.000625%7D%20)
![t = 277](https://tex.z-dn.net/?f=%20t%20%3D%20277%20)
For the continuously compounded interest, r =0.23%
![A = Pe^{rt}](https://tex.z-dn.net/?f=%20A%20%3D%20Pe%5E%7Brt%7D%20)
![2P = Pe^{0.0023t}](https://tex.z-dn.net/?f=%202P%20%3D%20Pe%5E%7B0.0023t%7D%20)
![2 = e^{0.0023t}](https://tex.z-dn.net/?f=%202%20%3D%20e%5E%7B0.0023t%7D%20)
![\ln 2 = \ln e^{0.0023t}](https://tex.z-dn.net/?f=%20%5Cln%202%20%3D%20%5Cln%20e%5E%7B0.0023t%7D%20)
![\ln 2 = 0.0023t](https://tex.z-dn.net/?f=%20%5Cln%202%20%3D%200.0023t%20)
![t = \dfrac {\ln 2}{0.0023}](https://tex.z-dn.net/?f=%20t%20%3D%20%5Cdfrac%20%7B%5Cln%202%7D%7B0.0023%7D%20)
![t = 301](https://tex.z-dn.net/?f=%20t%20%3D%20301%20)
The quarterly compounded doubles in 277 years.
The continuously compounded doubles in 301 years.
Answer: FYAB gives a better deal.
Fractional index means "xth root of". Negative index means a fraction. So together, what it really means is:
![\frac{1}{\sqrt[5]{32}} = \frac{1}{2}.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%5B5%5D%7B32%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D.)
The missing number is 225
225+10=235