An investor has $100,000 to invest in three types of bonds: short-term, intermediate-term, and long-term. How?
Posted by admin in Finance Sunday, 23 October 2011 01:40 2 Comments
An investor has $100,000 to invest in three types of bonds: short-term, intermediate-term, and long-term. How much should she invest in each type to satisfy the given conditions.? Short term bond pays 4% annually, intermediate term bonds pay 5% and a long term bonds pay 6% The investor wishes to realize a total annual income of 5.1% with equal amounts invested in short and intermediate term bonds
Let s = amount invested in short-term bonds, i = amount invested in intermediate-term bonds, l = amount invested in long-term bonds
Then:
i = s
s + i + l = $100,000
0.04s + 0.05i + 0.06l = 0.051 X $100,000
First, substitute s for i in the second equation, to get
s + s + l = $100,000, or
2s + l = $100,000
Next, substitute s for i in the second equation, to get
0.04s + 0.05s + 0.06l = 0.051 X $100,000
Now, since 2s + l = $100,000, then
l = $100,000 – 2s
Since l = $100,000 – 2s, and 0.04s + 0.05s + 0.06l = 0.051 X $100,000, then, by substitution,
0.04s + 0.05s + 0.06($100,000 – 2s) = 0.051 X $100,000
0.09s + $6,000 – 0.12s = $5,100 do arithmetic on both sides and distribute the factor of 0.06
0.09s – 0.12s = $5,100 – $6,000 subtract $6,000 from each side
-0.03s = -$900 simplify by doing arithmetic
s = -$900 / 0.03
s = $30,000
Since s = $30,000 and i = s, i = $30,000. Since s = $30,000 and i = $30,000 and s + i + l = $100,000, then l = $40,000.
Let’s check:
0.04 X $30,000 + 0.05 X $30,000 + 0.06 X $40,000 = $1,200 + $1,500 + $2,400 = $5,100
Short Term and Intermediate Term = $30,000 each
Long Term = $40,000