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

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

Part b)
`I=\$662.03`

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`