A) $53687.10
B) $68899.81
C) Yes
Explanation
A) George's money will follow the formula
![A=p(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3Dp%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
,
where p is the principal invested, r is the interest rate as a decimal number, n is the number of times per year the money is compounded, and t is the number of years.
This gives us
![A=20000(1+\frac{0.06}{4})^{5*4}=20000(1+0.015)^{20}=26937.10](https://tex.z-dn.net/?f=A%3D20000%281%2B%5Cfrac%7B0.06%7D%7B4%7D%29%5E%7B5%2A4%7D%3D20000%281%2B0.015%29%5E%7B20%7D%3D26937.10)
Jim's money follows the formula
A=p + prt, where p is the principal invested, r is the interest rate as a decimal number, and t is the number of years.
This gives us
A=20000+20000(0.0675)(5) = 26750
This gives us a total pooled of 26750+26937.10 = 53687.10
B) The pooled money will follow the formula
![A=p(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3Dp%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
,
where p is the principal invested, r is the interest rate as a decimal, n is the number of times per year the interest is compounded, and t is the number of years.
This gives us
![A=53687.10(1+\frac{0.05}{12})^{5*12}=68899.81](https://tex.z-dn.net/?f=A%3D53687.10%281%2B%5Cfrac%7B0.05%7D%7B12%7D%29%5E%7B5%2A12%7D%3D68899.81)
C) Since each man inherits 20000, this gives us a total of 40000. Using the compound interest formula above, we have
![A=40000(1+\frac{0.0675}{12})^{10*12}=78412.87](https://tex.z-dn.net/?f=A%3D40000%281%2B%5Cfrac%7B0.0675%7D%7B12%7D%29%5E%7B10%2A12%7D%3D78412.87)
This is more money than the two separate accounts being pooled, so yes, they should have done this.