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

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calculista calculista · Answer 1 · 2019-04-02T00:58:12+02:00

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 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

[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 years

in 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]