SOLUTION: Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term

Question 1009023: Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term bonds pay 5%, the intermediate-term bonds pay 6%, and the long-term bonds pay 7% simple interest per year. Mark wishes to realize a total annual income of 5.95%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = short range
y = intermediate range
z = long range.

x + y + z = 100,000

.05x + .06y + .07z = .0595 * 100,000 = 5950

x = y

replace y with x to get:

2x + z = 100,000
.11x + .07z = 5950

note that .11x is equivalent to .05*x + .06*x.

multiply both sides of the second equation by 100 and multiply both sides of the first equation by 7 to get:

14x + 7z = 700,000
11x + 7z = 595,000

subtract second equation from the first to get:

3x = 105,000

solve for x to get:

x = 35,000

in the first original equation of 2x + z = 100,000, replace x with 35,000 to get 2 * 35,000 + z = 100,000.

this becomes 70,000 + z = 100,000.

solve for z to get z = 30,000

in the second original equation of .11x + .07z = 5950, replace x with 35,000 and replace z with 30,000 to get .11 * 35,000 + .07 * 30,000 = 5950.

simplify to get 5950 = 5950.

this confirms the solution is correct.

.11 * x is equivalent to .05 * x + .06 * x

since y = x, this is equivalent to .05 * x + .06 * y

both x and y are equal to 35,000, so this is equivalent to .05 * 35,000 + .06 * 35,000.

you have:

.05 * 35,000 dollars in short term bonds + .06 * 35,000 in intermediate term bonds + .07 * 30,000 dollars in long term bonds.

the total money invested is 100,000.

the total interest earned is 5,950

5,950 / 100,000 = .0595

.0595 * 100 = 5.95%.

RELATED QUESTIONS
Mark has $100,000 to invest. His financial consultant advises him to diversify his... (answered by ikleyn,josgarithmetic)

Doris has $20,000 to invest. Her financial planner recommends that she diversify into... (answered by stanbon)

I NEED HELP SETTING UP THIS WORD PROBLEM: Tracy has $20,000 to invest. As her... (answered by solver91311,josmiceli)

A financial advisor advises Jennifer to invest her money equally in stocks and bonds. If... (answered by ikleyn)

A financial consultant wishes to invest up to a total of $30,000 in two types of... (answered by ikleyn)

Is it C? I want to check my answer. Topic: Financial Mathematics Mr. Slater... (answered by MathLover1)

A person has $50,000 to invest. As the person's financial consultant, you... (answered by ikleyn)

Jake has decided to invest in three business ventures. The total cost of investing in all (answered by mananth)

A person has 30,000 to invest. As the person's financial consultant, you recommend that... (answered by ankor@dixie-net.com)