Martin purchased some municipal bonds yieldi

Question

Martin purchased some municipal bonds yielding 8% annually and some certificates of deposit yielding 11% annually. If Martin's investment amounts to $23,000 and the annual income is $2230, how much money is invested in bonds
and how much is invested in certificates of deposit?

Answer 1

Simple Interest, i=Prt

We have 2 equations with separate interest (i), principle (P), and rate (r). t is equal at 1 year. 

i1=P1r1t        i2=P2r2t

The initial investment was equal to $23000.

P1+P2=23000

The total interest is $2230.

i1+i2=2230

We have too many unknowns. Let's get rid of 1 by solving i1+i2=2230 for i1

i1=2230-i2

Substitute it in our other equation i1=P1r1t

(2230-i2)=p1r1t

Now let's do the same thing with our other 2 equations. First solve for p2 from p1+p2=23000

p2=23000-p1

Sub into i2=p2r2t

i2=(23000-p1)r2t

Now let's solve each new equation for i2 so we can eliminate it and be left with 1 variable. 

i2=(23000-p1)r2t

i2=2230-p1r1t

These are equal now

2230-p1r1t=(23000-p1)r2t

solve for p1

p1=(23000r2t-2230)/(r2t-r1t)

plug in the numbers to get

p1=10000(bonds)

so then p2=13000

Answer 2

Let x = amount invested in CD's

 

Then, 23,000 - x = amount invested in bonds

 

Assuming simple interest (no compounding during the year), we have

 

  0.11x + 0.08(23,000 - x) = 2230

 

  0.11x + 1840 - 0.08x = 2230

 

  0.03x = 390

 

        x = $13,000

 

Invest $13,000 in CD's and $10,000 in municipal bonds.