Find the interest rates charged by the banks.
Answer to Problem 22P
The interest rate of the first bank and second bank is
Explanation of Solution
Given data:
Total amount borrowed
In First bank, uniform series payment at the end of each year
In Second bank, uniform series payment at the end of each month
Formula used:
Consider the following expression obtained from the payment details of first bank,
Here,
The equation (1) is rewritten with respect to the given values is,
Consider the following expression obtained from the payment details of second bank,
Here,
The equation (3) is rewritten with respect to the given values is,
Formula to calculate the present cost for the given uniform series payment is,
Formula to calculate the present cost for the given uniform series payment when the interest compounds
Calculation:
Case 1: Interest rate of first bank
Substitute the equation (5) in equation (2) and substitute
By using trial and error method, calculate the value of
(i) Interest rate of
Substitute
Reduce the equation as,
From the equation (8), it is clear that
(ii) Interest rate of
Substitute
Reduce the equation as,
From the equation (9), it is clear that
Case 2: Interest rate of second bank:
Substitute the equation (6) in equation (4), and substitute
Rewrite the equation as follows,
By using trial and error method, calculate the value of
(i) Interest rate of
Substitute
Reduce the equation as,
From the equation (11), it is clear that
(ii) Interest rate of
Substitute
Reduce the equation as,
From the equation (12), it is clear that
Therefore, from the analysis the interest rate of the first bank and second bank is
The second bank is highly preferable because it provides less interest rate than the first bank.
Conclusion:
Thus, the interest rate of the first bank and second bank is
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Chapter 20 Solutions
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