Answer:
a) $8 interest
b) 32% annual rate
Step-by-step explanation:
<h3>a)</h3>
The interest is the excess of the payment over the amount borrowed:
$58 -50 = $8 . . . amount of interest
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<h3>b)</h3>
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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<em>Additional comment</em>
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
