How much initially invested?

Question

Bill invests in a plan that has an APR of 4%. He invests three times as much in a plan that has an APR of 5%. If the total interest from the investments is $779 after one year, how much was invested in each plan?

Answer 1

A = p(1+rt)

 

So,

 (inv1) -->   p(1+.04*t) because we invest at rate r = 4%

 (inv2) --> 3p(1+.05*t) because we invest 3 times as much at rate r = 5% 

 

If t = 1. (After 1 year)

 (inv1) -->   p(1.04)

 (inv2) --> 3p(1.05)

 

A = 779,  (the interest gained)

 

So,

 

A = inv1 + inv2

 

779 = 1.04p+3.15p

 

Solve for p,

779/4.19 = p

185.92

 

That is the initial investment for 1.

 

If we multiply by 3 we get the initial investment of 557.75

 

That is the initial investmentfor 2