Question

george and jim were brother were brothers who were each left an inheritance of $20,000. George invested his money in an account for 5 years at an annual interst rate of 6% compounded quarterly,Jim invested his money for 5 years at an annual simple interest rate of 6.75%.at the end of the five years, they agreed to pool their accumulated principals into one account for a further 5 years with an annual interest rate of 5% compounded monthly. a. how much accumulated principal did George and Jim each have after 5 years? Hence determine how much money they had to pool. b. What was the accumulated principal of their pooled money at the end of the 10 year period. c. when George and Jim first recieved their inheritance, the executor of the will suggested that they pool their resources immediately for 10 years and invest in an account that paid an annual interest rate of 6.75% compounded monthly. in view of your answer in (a) and (b) above, should they have taken this advice? Explain.

Answer 1

A) $53687.10
B) $68899.81
C) Yes

Explanation
A) George's money will follow the formula 
$A=p(1+\frac{r}{n})^{nt}$,
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
$A=20000(1+\frac{0.06}{4})^{5*4}=20000(1+0.015)^{20}=26937.10$

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
$A=p(1+\frac{r}{n})^{nt}$, 
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
$A=53687.10(1+\frac{0.05}{12})^{5*12}=68899.81$

C) Since each man inherits 20000, this gives us a total of 40000.  Using the compound interest formula above, we have
$A=40000(1+\frac{0.0675}{12})^{10*12}=78412.87$

This is more money than the two separate accounts being pooled, so yes, they should have done this.