Question

Phyllis invested 50000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 2720 dollars. How much money did she invest at each rate?

Answer 1

Answer:

The amount invested at 5% was $39,000 and the amount invested at 7% was $11,000

Step-by-step 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 invested at 5%

50,000-x -----> the amount invested at 7%

so

$t=1\ year\\ I=\ 2,720\\r_1=0.05\\r_2=0.07\\P_1=\ x\\P_2=\ (50,000-x)$

substitute in the formula above

$2,720=x(0.05*1)+(50,000-x)(0.07*1)$

solve for x

$2,720=0.05x+3,500-0.07x$

$0.07x-0.05x=3,500-2,720\\0.02x=780\\x=\ 39,000$

$(50,000-x)=\ 11,000$

therefore

The amount invested at 5% was $39,000 and the amount invested at 7% was $11,000