find variable

Question

Casey is retiring and has $2.5 million to invest in stocks and bonds. Casey estimates that the stocks will have an average return of 9.5% and the bonds will pay 7% simple interest. Casey wants $210,000 per year to cover his living and travel expenses each year.

1-What variables are appropriate?
a- S (amount in bonds [in 1000s]) and B (interest rate)
b- S (amount in stocks [in 1000s]) and B (amount in bonds [in 1000s])
c- S (average return) and B (amount in bonds [in 1000s])
d- S (amount in stocks [in 1000s]) and B (average return)
e- S (average return) and B (interest rate)

 

2- Write a system of inequalities to show the possible amounts he could invest in each account.

 

a-returns =??

b-investment+ ??

 

Answer 1

s+b =2.5 x 10^6 = 2 1/2 million dollars

.095s +.07b = .21 x 10^6 = $210,000

two equations two unknowns solve by substitution elimination

s = 2.5 x 10^6 - b

.095(2.5 x 10^6 -b) + .07b = .21 x 10^6

9.5(2.5 x 10^6) - 9.5b + 7b = 21 x 10^6

2.5b = (9.5(2.5)-21) x 10^6

b = (9.5 -21/2.5) x 10^6 = (9.5-8.4) x 10^6 = 1.1 x 10^6 = $1.1 million invested in bonds

s =2.5 - 1.1 x 10^6 = $1.4 million invested in stocks

9.5% of 1.4 = 1.33 = $133000 return on stocks each year

7% of 1.1 = .77 = $77,000 return on bonds each year

total return = 133000+77000 = $210,000