Taylor has $32000 a part of which he invested at 5% and the remainder at 3%. His annual return on each investment is the same. At what rate would he have to invest all her money to get the same interest?

Taylor have to invest the total money at 3.75%

Step-by-step explanation:

Let the part of money invested at 5% be 'a' and the part of money invested at 3% be (32000-a).

To find (a):

The annual income for both the 5% and 3% investment is equal.

Interest = (amount x rate of interest x time) / 100

Interest for 5% rate on investment

Interest = (a x 5 x 1) / 100

Interest for 3% rate on investment

Interest = [ (32000-a) x 3 x 1]/100

Both the interests are equal so equate both the equations.

(a x 5 x 1) / 100 = [ (32000-a) x 3 x 1] / 100

5a = (32000-a) 3

5a = 96000-3a

8a = 96000

a = 96000/8

a = 12000

32000-a = 32000-12000

= 20000

The amount invested at 5% is $12000 and invested $20000 at 3%

Interest = (12000 x 5 x 1) / 100

= 60000/100

= $600

Interest = (20000 x 3 x 1) / 100

= 60000/100

= $600

Total interest = $1200

To find the rate at which the total money is to be invested to get the same annual income.

1200 = (32000 x rate x 1) / 100

1200 x 100 = 32000 x rate x 1

120000 = 32000 x rate

120000/32000 = rate

Rate = 3.75%

Taylor have to invest the total money at 3.75% to get the same annual income