Question

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

Answer 1

Explanation:

Let x be the investment at 5.25% and y at 4%

Then we have

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

We have to solve this system to get x and y

Multiply I equation by 4

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

12000 should be invested in 5.25% and 13000 in 4% interest.

Answer 2

The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000

Explanation:

we know that

The simple interest formula is equal to

`I=P(rt)`

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

Let

x ------> the amount of money that should be invested at the rate of 5.25%

25,000-x -----> the amount money that should be invested at the rate of 4%

in this problem we have

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

substitute in the formula above

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

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

Solve for 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`

therefore

The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000