Question

You have agreed to borrow $50 and after six months pay back $58. how much interest are you paying? what is the interest rate?

Answer 1

Answer:

  a) $8 interest

  b) 32% annual rate

Step-by-step explanation:

a)

The interest is the excess of the payment over the amount borrowed:

  $58 -50 = $8 . . . amount of interest

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b)

The interest rate is the fraction of the original amount that is interest:

  8/50 = 16/100 = 16% . . . . 6-month rate

Usually, we express the rate as an annual rate, so we need to divide this percentage by the number of years. 6 months is 1/2 year, so ...

  r = 16%/(1/2) = 32% . . . . annual interest rate

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Additional comment

The amount of interest is computed using the formula ...

  I = Prt . . . . . P is the principal borrowed; r is the annual rate; t is the number of years

We can use this to find r, the annual rate:

  I/(Pt) = r . . . . . divide by the coefficient of r

  r = 8/(50·1/2) = 8/25 = 32/100 = 32% . . . . annual rate