Question

A portion of $7200 is invested at a 4% annual return, while the remainder is invested at a 5% annual return. If the annual income from both portions is the same, what is the total income from the two investments?

Answer 1

Let portion of sum is invested at 4% = x

Portion invested at 5% will be = (7200 - x)

Annual income is same from both the parts so,

4% of x = 5% of (7200 - x)

4x/100 = 5/100 (7200 - x)

4x = 36000 - 5x

4x + 5x = 36000

9x = 36000

x = 36000/9 = 4000

Part invested at 4% = 4000

Part invested at 5% = (7200 - 4000) = 3200

Answer 2

Therefore the total income from the 2 investments is $320.

Given:

Total amount invested = $ 7200

A portion of $7200 is invested at a 4% annual return and the remainder is invested at a 5 % rate of interest.

Annual income from both portions is the same.

To Find:

The Total income from the 2 investments.

Solution:

The given question can be solved as shown below.

Let $ x is invested at a 4% annual return

Then the annual income from that portion = $0.04x

Let the remainder ( $ 7200 - $ x ) is invested at a 5 % rate of interest.

Then the annual income from the remaining portion = $0.05 ( 7200-x )

Given that the annual income from both investments is the same.

⇒ 0.04x = 0.05 ( 7200 - x )

⇒ 0.04x = 360 - 0.05x

⇒ 0.04x + 0.05x = 360

⇒ 0.09x = 360

⇒ x = 360/0.09 = 4000

The portion which is invested with 4% annual interest = x = 4000

⇒ Then Annual income from this portion = 0.04 × 4000 = $160

The remaining portion which is invested with 5%  annual interest = ( 7200 -4000 ) = 3200

⇒ Then the annual income from the remaining portion = 0.05 × 3200 = $160

Hence the total income from the 2 investments = 160 + 160 = 320

Therefore the total income from the 2 investments is $320.

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