the simple interest I ( in dollars) for a savings account is jointly proportional to the product of the time t (in years) and the principal P (in dollars). After five months, the interest on a principal of $3892 is $92. a) find the constant of variation.b) what will the interest be after 3 years
Accepted Solution
A:
Answer:Part a) The constant of variation is [tex]r=0.0567[/tex] or [tex]r=5.67\%[/tex]Part b) [tex]I=\$662.03[/tex]
Step-by-step explanation:Part a) Find the constant of variation.we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
In this linear direct variation the constant r represent the constant of proportionalitywhere
I is the Interest Value
P is the Principal amount of money to be invested
r is the rate of interest t is Number of Time Periods
in this problem we have
[tex]t=5/12\ years\\ P=\$3,892\\ I=\$92\\r=?[/tex]
substitute the values and solve for r[tex]92=3,892(r(5/12))[/tex]
[tex]r=(92*12)/(3,892*5)[/tex][tex]r=0.0567[/tex]Part b) what will the interest be after 3 yearsin this part we have
[tex]t=3\ years\\ P=\$3,892\\ I=?\\r=0.0567[/tex]
substitute the values [tex]I=3,892(0.0567*3)=\$662.03[/tex]