How much money should be invested in the corporate bond fund

How much money should be invested in the corporate bond fund if the total annual return between both investment in $120,000?

Solution

Let the amounts invested in the corporate bond fund paying 3 % interest and the municipal bond fund paying 6 % interest be x and y million dollars respectively. Then, we have x + y = 3. ...(1)

Also, the annual returns on the investments in the corporate bond fund and the municipal bond funds are 3 * 3 % and y*6% i. e. 3x/100 and 6y /100 respectively. Since the annual return on the total investment is $ 120000, we have 3x/100 + 6y/100 = 0.12 ( $ 120000 = $ 0.12 million; x and y are in millions of dollars). or, on multiplying both the sides by 100, we have 3x + 6y = 12 or, x + 2y = 4... (2)

From the 1st equation, we have x + y = 3 or, x = 3 - y. On substituting x = 3 - y in the 2nd equation, we get 3 - y + 2y = 4 or, y = 4 - 3 = 1. Then x = 3 - y = 2.Thus, to get an annual return of $ 120000, $ 2 million have to be invested in the corporate bond fund paying 3 % interest and $ 1 million has to be invested in the municipal bond fund paying 6 % interest.