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
Want to see more full solutions like this?
Chapter 20 Solutions
Engineering Fundamentals
- A man will deposit 200 with a savings bank at the beginning of each 3 months for 9 years. If the bank pays interest at the rate of 5.5% quarterly, find the sum to his credit just after the last deposit. *written solution pleasearrow_forwardCompute the future value of a $3500 deposit, after eight years, in an account that pays a simple interest rate of 5%. How much interest will be paid to this account?arrow_forward#20,000.00 borrowed today for 2 years at 5% compound interest will result in how much total interest at the end of Year 2?arrow_forward
- . Determine the exact simple interest on P 5,000.00 for the period from May 16 2016 to October 18, 2022 if the rate of interest is 15%arrow_forwardWhich is a better choice in buying a washing machine worth P12,700.00? * A. Avail of the instalment plan which requires payment of #850.00 a month for 18 months B. Borrow from a lending company that charges 12 1/4% simple interest payable in 1 year and 6 months C. Borrow from a lending firm offering 12% compounded quarterly payable in 1 year and 6 months D. Borrow from a lending firm offering 12% compounded monthly payable in 1 year and 6 monthsarrow_forwardCompute the future value of a $3500 deposit made today, after eight years, in an account that pays an interest rate of 5% that compounds annually. How much interest will be paid to this account?arrow_forward
- 3 ENGINEERING ECONOMICS: ANNUITY. Show complete solution and INCLUDE CASH FLOW DIAGRAM. Write legiblyarrow_forward1.You deposit $50,000 into a fund that pays 5% per year compounded annually. You plan to make the following withdrawals. You withdraw $X one year from now, $2X three years from now, and $3X five years from now. If the last withdrawal depletes the fund, what is the value of X?arrow_forwardA gasoline engine is available on installment basis with a down payment of 10,688 and 2,328 at the end of each month for one year. What is the cash price of the engine if interest is set at 9% compounded monthly if payments are done every beginning of the month?pls show the formula and complete solution :(arrow_forward
- Company B has a P5M loan for a new security system it just bought. The annual payment is P444,000 and the interest rate is 8% per year for 30 years. Your company decides that it can afford to pay P500,000 per year. After how many payments (years) will the loan be paid off?arrow_forwardPlease give answer fastarrow_forwardQ3:How much money must you deposit in year 6 if you deposit $5000 now and you want to have $12,000 at the end of year 11? Assume your deposits earn interest at 6% per year. [40 marks]arrow_forward
- Engineering Fundamentals: An Introduction to Engi...Civil EngineeringISBN:9781305084766Author:Saeed MoaveniPublisher:Cengage LearningFundamentals Of Construction EstimatingCivil EngineeringISBN:9781337399395Author:Pratt, David J.Publisher:Cengage,