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13 days ago

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A trust fund worth $25,000 is invested in two different portfolios, this year, one portfolio is expected to earn 5.25% interest

and the other is expected to earn 4%. Plans are for the total interest on the fund to be $1,150 in one year. How much money should be invested at each rate

2 answers:

Leona [4.1K]13 days ago

8 0

Answer:

Step-by-step explanation:

Let x denote the amount invested at 5.25%, and y the amount invested at 4%.

The system of equations is

$x+y =25000\\5.25x+4y = 115000$

Solving this system will determine values for x and y.

Multiply the first equation by 4:

$100000=4x+4y\\115000=5.25x+4y\\-----------------------------\\15000 = 1.25x\\x = 12000\\y =25000-12000 = 13000$

The solution is an investment of $12,000 at 5.25% and $13,000 at 4% interest rates.

Leona [4.1K]13 days ago

6 0

Answer:

A sum of $12,000 should be allocated at an interest rate of 5.25%, while $13,000 should be put in at 4%.

Step-by-step explanation:

Recall that

The simple interest formula is given by

$I=P(rt)$

where

I represents the total interest earned,

P is the initial investment,

r stands for the interest rate, and

t is the number of time periods.

Define

x as the amount invested at 5.25%,

and (25,000 - x) as the amount put in at 4%.

From the problem,

$t=1\ year\\ P_1=\$x\\P_2=\$(25,000-x)\\r_1=0.0525\\r_2=0.04\\I=\$1,150$

Plugging these into the formula:

$I=P_1(r_1t)+P_2(r_2t)$

$1,150=x(0.0525*1)+(25,000-x)(0.04*1)$

Now, isolate x:

$1,150=0.0525x+1,000-0.04x$

$0.0525x-0.04x=1,150-1,000$

$0.0125x=150$

$x=\$12,000$

$|$25,000-x=\$13,000$

Hence, investing $12,000 at 5.25% and $13,000 at 4% meets the required interest condition.

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