Question

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​

Answer 1

Answer:

Part a) The constant of variation is $r=0.0567$ or $r=5.67\%$

Part b) $I=\ 662.03$

Step-by-step explanation:

Part a) Find the constant of variation.

we know that

The simple interest formula is equal to

$I=P(rt)$

In this linear direct variation the constant r represent the constant of proportionality

where

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

$t=5/12\ years\\ P=\ 3,892\\ I=\ 92\\r=?$

substitute the values and solve for r

$92=3,892(r(5/12))$

$r=(92*12)/(3,892*5)$

$r=0.0567$

Part b) what will the interest be after 3 years

in this part we have

$t=3\ years\\ P=\ 3,892\\ I=?\\r=0.0567$

substitute the values

$I=3,892(0.0567*3)=\ 662.03$