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

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]