Question

Lakisha has a total of $8000 to invest in two accounts for 1 year. One pays 5% simple interest, and the other pays 6% simple interest. How much should she invest in each account so the total interest earned is $438?

Answer 1

Let the amount invested in the first account be x and let the amount invested in the second be 8000 - x
We have PRT/100 where P is her principal and r, her rate and t, the time
So in the first account I = x * 5 * 1/100
I = 5x/100
On the other hand if she gets 6% interest in the second account, we have I = PRT/100
So we have I = (8000 - x) * 6 * 1/ 100
I = (48000 - 6x)/100
But the combined interst is 438 so we have
5x/100 + (48, 000 - 6x)/100 = 438
Multiply through by 100
5x + 48, 000 - 6x = 43800
-x = 43800 - 48, 000
-x = -4200
Hence x = 4200. She will have to invest 8000 - 4200 in the second account which is 3800

Answer 2

Simple interest rate is given by:
I=(PRT)/100
let the amount invested in 5% S.I. be $x and amount invested in 6% S.I. be $(8000-x)
Interest obtained from 5% will be:
I=5/100×1×x=0.05x

Interest obtained from 6% will be:
I=6/100×1×(8000-x)=0.06(8000-x)
therefore total interest earned from the to schemes will be:
0.05x+0.06(8000-x)=438
solving for x we obtain:
0.05x+480-0.06x=438
0.05x-0.06x=438-480
-0.01x=-42
x=-42/(-0.01)
x=$4200
hence amount invested in 5% S.I. is $4200 and amount invested in 6% S.I. is (8000-4200)=$3800