Answer:
Part 1) [tex]\$106[/tex]
Part 2) [tex]\$53[/tex]
Part 3) [tex]\$212[/tex]
Part 4) [tex]\$132.50[/tex]
Part 5) [tex]\$1.06x[/tex]
Step-by-step explanation:
we have
Money in a particular savings account increases by about 6% after a year.
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Part 1) How much money will be in the account after one year if the initial amount is $100
in this problem we have
[tex]t=1\ year\\ P=\$100\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=100(1+0.06*1)[/tex]
[tex]A=100(1.06)[/tex]
[tex]A=\$106[/tex]
Part 2) How much money will be in the account after one year if the initial amount is $50
in this problem we have
[tex]t=1\ year\\ P=\$50\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=50(1+0.06*1)[/tex]
[tex]A=50(1.06)[/tex]
[tex]A=\$53[/tex]
Part 3) How much money will be in the account after one year if the initial amount is $200
in this problem we have
[tex]t=1\ year\\ P=\$200\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=200(1+0.06*1)[/tex]
[tex]A=200(1.06)[/tex]
[tex]A=\$212[/tex]
Part 4) How much money will be in the account after one year if the initial amount is $125
in this problem we have
[tex]t=1\ year\\ P=\$125\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=125(1+0.06*1)[/tex]
[tex]A=125(1.06)[/tex]
[tex]A=\$132.50[/tex]
Part 5) How much money will be in the account after one year if the initial amount is $x
in this problem we have
[tex]t=1\ year\\ P=\$x\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=x(1+0.06*1)[/tex]
[tex]A=x(1.06)[/tex]
[tex]A=\$1.06x[/tex]
