Question

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 3%, the intermediate-term bonds pay 5%, and the long-term bonds pay 7% simple interest per year. Mark wishes to realize a total annual income of 4.9%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond?

Answer 1

Answer:

for short range total invest is  = 0.03 *35000 = $1050

for intermediate range invest is  = 0.05 *35000 = $1750

for long range invest is  = 0.07 * 30000 = 2100

Explanation:

let x be the short raange

y be the intermediate range

z be the long range

from data given in thee question we have

x+ y+ z = 100,000 .....1

0.03 x + 0.05 y + 0.07 z = 0.049 *100,000 .....2

 from question x = y  so

equation 1 becomes

2x + z = 100,000  ....3

equation 2 becomes

0.08 x + 0.07 z = 4900 ... 4

multiply 3 eq by 7 and 4 eq by 100

14 x + 7z = 700,000 ...5

8x + 7z = 490,000 .....6

from 5 and 6 we have

x =35000

y = 35000

z = 30,000

for short range total invest is  = 0.03 *35000 = $1050

for intermediate range invest is  = 0.05 *35000 = $1750

for long range invest is  = 0.07 * 30000 = 2100