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Difference between revisions of "1954 AHSME Problems/Problem 33"

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==Solution==
 
==Solution==
  
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The borrower pays <math>\textdollar{120}</math> in a single year for a loan of <math>\textdollar{114}</math>. This means that the bank charges an interest of <math>\textdollar{6}</math> for a loan of <math>\textdollar{114}</math> over a single year, so that the annual interest rate is <math>100*\frac{\textdollar{6}}{\textdollar{114}} = \frac{100}{19} \approx 5</math> percentage points. Therefore, our answer is <math>\boxed{\text{(A)}</math> and we are done.
+
The borrower pays <math>\textdollar{120}</math> in a single year for a loan of <math>\textdollar{114}</math>. This means that the bank charges an interest of <math>\textdollar{6}</math> for a loan of <math>\textdollar{114}</math> over a single year, so that the annual interest rate is <math>100*\frac{\textdollar{6}}{\textdollar{114}} = \frac{100}{19} \approx 5</math> percentage points. Therefore, our answer is <math>\boxed{\text{(A)}}</math> and we are done.
  
 
==See Also==
 
==See Also==

Latest revision as of 15:51, 21 August 2020

A bank charges $\textdollar{6}$ for a loan of $\textdollar{120}$. The borrower receives $\textdollar{114}$ and repays the loan in $12$ easy installments of $\textdollar{10}$ a month. The interest rate is approximately:

$\textbf{(A)}\ 5 \% \qquad \textbf{(B)}\ 6 \% \qquad \textbf{(C)}\ 7 \% \qquad \textbf{(D)}\ 9\% \qquad \textbf{(E)}\ 15 \%$

Solution

The borrower pays $\textdollar{120}$ in a single year for a loan of $\textdollar{114}$. This means that the bank charges an interest of $\textdollar{6}$ for a loan of $\textdollar{114}$ over a single year, so that the annual interest rate is $100*\frac{\textdollar{6}}{\textdollar{114}} = \frac{100}{19} \approx 5$ percentage points. Therefore, our answer is $\boxed{\text{(A)}}$ and we are done.

See Also

1954 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 32 		Followed by
Problem 34
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions

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