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?
Answers
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
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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