1954 AMC 12 Problem 33

Question

A bank charges

\$6

for a loan of

\$120.

The borrower receives

\$114

and repays the loan in

12

installments of

\$10

a month. The interest rate is approximately:

5\%

6\%

7\%

9\%

15\%

The

\$6

charge is interest on a balance that decreases by

\$10

each month

Approximate the average outstanding principal by the average of

\$120

and

\$10

The balance decreases in equal

\$10

steps from

\$120

to

\$10,

so its average outstanding value is approximately

\frac{120+10}{2}=65.

The annual charge is therefore about

\frac6{65}\cdot100\%\approx9.2\%.

The nearest choice is

9\%.

Thus, the correct answer is D.

Problem 33 in other years