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
