Question

Philippa took out a $860 discounted loan for a period of m months at a simple interest rate of 6%. The amount she actually received into her bank account was $838.50. Calculate the value of m.

Answer 1

Answer:

m = 16.25 months

Step-by-step explanation:

To find the value for m, we first have to consider the formula for calculating simple interest.

The formula that we generally use is:

$I = Prt$

Now we have to find the value for t as it is not given.

We now define the different variables that we do have.

P = 860

I = 838.50

r = 6% or 0.06

t = ?

First we substitute the value that we do have in the formula.

838.50 = 860 (0.06) (t)

838.50 = 51.6 (t)

838.50 = 51.6t

Now we have to divide both sides by 51.6 to find the value of t.

$\dfrac{838.50}{51.6}=\dfrac{51.6t}{51.6}$

t = 16.25

Now that we have all the values, we can check if the number months is correct by doing the formula again.

$I = Prt$

$I = 860 (0.06)(16.25)$

$I = 860 (0.975)$

$I = 838.50$

Answer 2

Answer:

5 Months

Step-by-step explanation:

For this calculation we use the fact that the total interest is $860 − $838.50 = $21.50. Therefore using  I = Prt,

we get  $21.50 = $860 × 0.06 × t.

Solving this for t gives t = 0.416 =512. Hence m = 5.