MATH SOLVE

2 months ago

Q:
# Last year, Susan had 10,000 to invest. She invested some of it in an account that paid 6% simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of %560 in interest. How much did she invest in each account?

Accepted Solution

A:

Answer:In the account that paid 6% Susan invest [tex]\$6,000[/tex]In the account that paid 5% Susan invest [tex]\$4,000[/tex]Step-by-step explanation:we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest Β t is Number of Time Periods
Part a) account that paid 6% simple interest per yearin this problem we have
[tex]t=1\ years\\ P=\$x\\r=0.06[/tex]
substitute in the formula above
[tex]I1=x(0.06*1)[/tex]
[tex]I1=0.06x[/tex]
Part b) account that paid 5% simple interest per yearin this problem we have
[tex]t=1\ years\\ P=\$10,000-\$x\\r=0.05[/tex]
substitute in the formula above
[tex]I2=(10,000-x)(0.05*1)[/tex]
[tex]I2=500-0.05x[/tex]
we know that[tex]I1+I2=\$560[/tex]substitute and solve for x[tex]0.06x+500-0.05x=560[/tex][tex]0.01x=560-500[/tex][tex]0.01x=60[/tex][tex]x=\$6.000[/tex]thereforeIn the account that paid 6% Susan invest [tex]\$6,000[/tex]In the account that paid 5% Susan invest [tex]\$4,000[/tex]