Question

Santiago receives $177 per year in simple intrest from three investments. Part is invested at 2%, Part at 3% and at 4%. There is $500 more invested at 3% than at 2%. The amount invested at 4% is three times the amount invested at 3%. Find the amount invested at each rate.

Answer 1

Assume that the amount invested at 3% is x

∵ The amount invested in 3% is $500 more than the amount invested at 2%

∴ The amount invested at 2% = x - 500

∵ The amount invested at 4% is 3 times the amount invested at 3%

∴ The amount invested at 4% = 3x

∵ The rule of the simple interest is I = PRT, where

→ P is the amount invested

→ R is the rate in decimal

→ T is the time

Since he received $177 per year

∴ I = 177

∴ T = 1

∵ R1 = 2% = 2/100 = 0.02

∵ R2 = 3% = 3/100 = 0.03

∵ R3 = 4% = 4/100 = 0.04

∵ P1 = (x - 500)

∵ P2 = x

∵ P3 = 3x

$\therefore0.02(x-500)+0.03(x)+0.04(3x)=177$

Let us solve it to find x

$\because0.02x-10+0.03x+0.12x=177$

Add the like terms

$\begin{gathered} \therefore(0.02x+0.03x+0.12x)-10=177 \\ \therefore0.17x-10=177 \end{gathered}$

Add 10 to both sides

$\begin{gathered} 0.17x-10+10=177+10 \\ 0.17x=187 \end{gathered}$

Divide both sides by 0.17

$\begin{gathered} \frac{0.17x}{0.17}=\frac{187}{0.17} \\ x=1100 \end{gathered}$

He invested 1100 - 500 = 600 at 2%

He invested 1100 at 3%

He invested 3(1100) = 0033 at 4%

The answer is:

P1 = $600

P2 = $1100

P3 = $3300