an investment of $3000 is made at an annual simple interest rate of 5%.?

Question

how much additional money must be invested at an annual simple interest rate of 9% so that the total annual interest earned is 7.5% of the total investment.

explain the answer

Answer 1

let x = additional investment
3000(0.05) + 0.09 x = 0.075 (3000 + x)
150 + 0.09 x = 225 + 0,075 x
0.015 x = 75
x = 5000 in dollars

Answer 2

Let P be the amount needed.

We have 3000 x 5/100 + P x 9/100 = (3000 + P) x 7.5/100

We can cancel out the 100 in the denominator as it is common.

3000 x 5 + 9P = 3000 x 7.5 + 7.5 P

9P - 7.5 P = 3000 x (7.5 - 5)

1.5 P = 3000 x 2.5 = 7500

P = 7500 / 1.5 = 5000

So, 5000 dollars at 9% is needed. Let us check the solution.

3000 x 5 + 5000 x 9 = 8000 x 7.5

1500 + 4500 = 6000

Since LHS and RHS are equal, our solution is correct.

Answer 3

Underperforming money -> $3000 @ 5% interest.

Underperformance = $3000 @ 2.5% interest. That's $75/year.

Overperforming money = x @ 9%.

Overperformance = x @ 1.5% interest.

Overperformance needs to equal underperformance. Thus x @1.5% interest has to equal $75.

Multiply by 2/3, and you get x@1% = $50.

X is therefore $5000.

CHECK:
$5000 @ 9% interest => $450/year
$3000 @ 5% interest => $150/year
$8000 total investment => $600/year investment.
$8000 @7.5% interest would be $600.

Answer 4

interest earned = principal* annual interest rate* time in years / 100
an investment of $3000 made at an annual simple interest rate of 5% will earn an interest amount of $150 in one year.
let additional investment be R
n investment of $R is made at an annual simple interest rate of 9% will earn an interest amount of $9R/100 in one year

if effective rate has to be 7.5%, interest amount earned on total investment will be $(3000+R)(7.5)/100

$150 + $9R/100 = $(3000+R)(7.5)/100
15000 + 9R = 22500 + 7.5R
1.5R =7500
R = 7500/1.5 = 75000/ 15
R = 5000

so an additional $5000 needs to be invested at 9%

Answer 5

The answer is $ 5000 to be invested at 9% to get a total return of 7.5%

Let me explain the process.

Let us assume that the total Investment is 100, then,

Investment of 37.50 @ 5% will yield 1.875% of Total Investment (37.50 * 5%)
&
Investment of 62.50 @ 9% will yield 5.625% of Total Investment (62.50 * 9%)

1.875% + 5.625% = 7.50 %

Now $3000 = 37.50 % of Investment then what is the total

3000/37.50*100 = 8000,

So investment of $5000 has to be made @ 9% to get a total yield of 7.5% on the investment.

Solution

3000 * 5% = $ 150
5000 * 9% = $ 450
---------
$ 600

600/800*100 = 7.5%

Answer 6

let amount1(t) = amount of investment placed at 5% simple at time t
amount2(t) = amount of investment placed at 9% simple at time t


at time t:
amount1(t) = $3000 *(1 + 0.05t)
amount2(t) = amount2(0)*(1 + 0.09t)

3000*0.05t + amount2(0)*0.09t = 0.075t*(3000 + amount2(0))
dividing by t, amd multiplying the amounts
150 + 0.09*amount2(0) = 225 + 0.075*amount2(0)
amount2(0) = (225 - 150)/(0.09 - 0.075)
amount2(0) = 5000

so you must have an additional $5000 invested at 9% simple interest so that the total interest earned is 7.5% of the total investment