Question

John inherited $25,000 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund. After one year, he received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutual fund paid 8% annually. There was $6,000 more invested in the bonds than the mutual funds. Find the amount John invested in each category.​

Answer 1

Answer:

The amount of money invested in the money market account = 15000

The amount of money invested in mutual fund = 8000

The amount of money invested in municipal bonds = 2000

Ratio = 15:8:2

Step-by-step explanation:

$\green{\ggg}\red{\underline{Question:-}}$

John inherited $25,000 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund. After one year, he received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutual fund paid 8% annually. There was $6,000 more invested in the bonds than the mutual funds. Find the amount John invested in each category?

$\green{\ggg}\red{\underline{Solution:-}}$

Let the amount of money invested in the money market account = $p_1$

Let the amount of money invested in mutual fund = $p_2$

Let the amount of money invested in municipal bonds = $p_3$

$\bold{According\:to\:question,}$

$\Rightarrow p_1+p_2+p_3 = 25000....( 1)$

$\Rightarrow p_2-p_3 = 6000...(2)$

$\Rightarrow 6p_1+7p_2+8p_2 = 162 \times 10^3\:\:...(3)$

On,subtracting (1) from (3)

____________________

$\:6p_1 +7p_2+8p_3=162000$

$6p_1$ ∓ $6p_2$ ∓ $6p_3$ = $150000$

= $0+p_2+2p_3$     = 14000    ....(eq 1)

____________________

After subtracting the (1) from (3) we got answer that,

$p_2+p_3 = 12000$

Now, we should subtract $p_2+p_3 = 14000$ from (equ.2)

_________________

$p_2+2p_3 = 14000$

-$p_2$  ∓ $p_3$  $= 6000$

$= 0+3p_3 = 8000$    ...(eq 2 )

________________

$3p_3 = 8000$

-$2p_3$ $= 6000$

= $p_3 = 2000$    ...(eq 3 )

_______________

We got answers,

$\bold{p_1 = 15000} \:\:\: ...from(1)$

$\bold{p_2 = 8000}\:\:\:\:...from(2)$

$\bold{p_3 = 2000} \: \: \: \: \:... from(3)$

Ratio = 15:8:2

The amount of money invested in the money market account = 15000

The amount of money invested in mutual fund = 8000

The amount of money invested in municipal bonds = 2000

$\red{:\longrightarrow}\boxed{\orange{Ratio = 15:8:2}}$