After graduation, you start working as the financial officer for a start up non government organization helping street children...Your organization has received a donation of 20 million...

After graduation, you start working as the financial officer for a start up non government organization helping street children...

Your organization has received a donation of 20 million pesos from a philanthropist. If your institution needs 500,000 PHP annually for operating expenses, how much of the donation will you invest in mutual funds and treasury bills if they respectively earn 3% and 2% annually. Solve using two variables. (Assume the money has to be invested in both types of investment for security reasons).

Use the format Given, required, solution, checking, and final answer.

Asked on by spock14

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thilina-g | College Teacher | (Level 1) Educator

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Given:

Total amount of money = 20000000

The interest needed annually = 500000

The annual interest rate in mutual funds = 3%

The annual interest rate in treasury bills = 1%

Required:

The fraction of donation to be invested in each investment method.

Solution:

Let the fraction of donation which is to be invested in mutual funds be P and the other fraction be Q.

Then P + Q = 1 -------> Equation 1

 

The amount to be invested in mutual funds = 20000000 * P

The amount to be invested in treasury bills = 20000000 * Q

 

The annual interest from mutual funds  = `20000000*P*(3/100)`

                                                        = 600000P

The annual interest from treasury bills  = 20000000*Q*(2/100)

                                                        = 400000Q

 

But we know the total interest should be 500000.


Therefore,

600000P + 400000Q = 500000  --------Equation 2

 

Solving equation 1 and equation2 would give you,

P =  0.5   and Q = 0.5

The fractions to be invested in mutual funds are 1/2 and in treasury bill is 1/2.

Therefore, exactly half of the donation should go to mutual funds and other half should go to treasury bills.

 

Checking:

The amount to be invested in mutual funds = 20000000 * 0.5

                                                              = 10000000

The interest from mutual funds                  = 10000000 * (3/100)

                                                              = 300000

The amount to be invested in treasury bills = 20000000 * 0.5

                                                              = 10000000

The interest from treasury bills                  = 10000000 * (2/100)

                                                              = 200000

The total interest is = 300000+200000 = 500000

Therefore the answer is correct.

 

Final answer:

Half (1/2) of the donation that is 10 million should be invested in mutual funds and other half that is 10 million should be invested in treasury bills.

 

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