simple interest

Question

How can $56,000 be invested, part at 4% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts is equal at the end of the year

Answer 1

You split the amount $56000 into two parts:

first part x for interest 0.04

second part (56000-x) for interest 0.1

At the end of the year you get balance for each.

Let first balance be A, second be B.

The earned amount for both is the same.

The used equation is:

Balance=principal(1+interest) since the time is 1 year.

Earned amount of the first is:

x(1+0.04)-x  .....(1)

Similarly for the second:

(56000-x)(1+0.1)-(56000-x)......(2)

Set (1) and (2) equal:

x(1+0.04)-x = (56000-x)(1+0.1)-(56000-x)

Simplifying:

1.04x-x=(56000-x)(1.1)-56000+x

0.04x=61600-1.1x-56000+x

0.04x=5600-0.1x

0.04x+0.1x=5600

0.14x=5600

x=5600/0.14

x=40,000.  This is the first part of investment for 0.04 interest and

56000-40000=16000 the second part for 0.1 interest.

the earned amount for each is:

40000(1+0.04) -40000= $1600

16000(1+0.1) -(16000)=$1600