Question

$5,000 is invested at 3% interest. How much money must be invested at 5% interest so that the total interest from the two investments is $275 after one year?

Answer 1

Simple interest.
I=Prt
where for the first equation at 3%
i=Interest=unknown
P=Principle starting money=5,000
r=rate=.03 (because we divide the 3% by 100 to get our usable number)
t=time in years=1

And we want to know how much is needed for 5%
We will add what we get from 3% to an unknown (x) and solve to find what will be needed for their combined number to be 275.
I(3%)=(5,000)(.03)(1)
i(3%)=150
We definitely get 150 from 3% interested. How much money will we have to invest at 5% to get a total interest of 275.
First find how much interest will we need from the 5% investment.

i(3%+5%)
150+x=275
subtract 150 from both sides
x=125
We will need a rate of 5% to get 125 in interest.

So now we do the I=Prt backwards with new information to find P need at 5%.
I=125
P=unknown
r=.05
t=1
125=P(.05)(1)
divide by .05
P=2500

2500 must be invested at 5% interest so that the combined interest of the 3% and 5% will be 275.