a man would like to invest 50000 pesos in government bonds and stocks that will give an overall annual return of 5%.

Question

a man would like to invest 50000 pesos in government bonds and stocks that will give an overall annual return of 5%. the money to be invested in government bonds will give an annual return of 4 and 1/2 percent and the stocks of about 6% annual return. the investment are in units of 100 pesos each. if he desires to keep his stocks investment to a minimum in order to reduce his risk, determine how many government bonds and how many stocks should he purchase?

Answer 1

You have to figure out how much to put into each kind of investment.  So first assign a variable name to each:

 

x = the amount to invest in government bonds.

y = the amount to invest in stocks.

 

So immediately you know that x + y = 50000

 

Now, figure out the total return from each investment:

 

The return from bonds is .045x (4.5% of x)

The return from stocks is .06y (6% of y)

 

So the total return from both will be .045x + .06y. 

 

You want this to be equal to 5%.  So...

 

(.045x + .06y) / 50000 = .05.

 

Now you have two equations in two unknowns:

 

x + y = 50000

(.045x + .06y) / 50000 = .05

 

Let's solve using subsitution.

 

Find an expression for y from the first equation:

y = 50000 - x

 

Substitute this into the second equation:

(.045x + .06 (50000 - x)) / 50000 = .05

 

Simplify:

(.045x + 3000 -.06x) / 50000 = .05

(3000 - .015x) / 50000 = .05

3000 - .015x = .05 * 50000

3000 - .015x = 2500

 

Add .015x to both sides and subtract 2500 from both sides:

500 = .015x

 

500 / .015 = x

33333.333 = x

 

This is the amount to invest in bonds. Since y = 50000 - x, y = 16666.666, which is the amount to invest in stocks.

 

But since the investment units are in blocks of 100 pesos, you have to round these off to a multiple of 100.  You could round to the NEAREST 100, which would give:

 

Bonds: 33300

Stocks: 16700

 

But if you want to keep the investment in stocks lower to reduce risk, you could round stocks DOWN:

 

Bonds: 33400

Stocks: 16600