To calculate: The faster payment of the loan by Person X if he makes a monthly payment of $225 with his new card and what happens if Person X has 2% of fee charged on any of his transferred balance
Introduction:
The time taken for the repayment of the loan is termed as the number of periods. It is denoted by “t”.
Answer to Problem 69QP
Person X makes the payment faster by 45.10 months and if Person X is charged with a fee of 2% then he takes to pay off the card by 43.28 months.
Explanation of Solution
Given information:
The Christmas ski vacation of person X was good but it ran over the budget. However, everything is not lost. Person X received a mail that states to transfer $12,000 from the current credit card that charges 18.6% of an annual rate and the new credit card of 9.2% charge. The monthly payment made by Person X with his new card is $25. It is assumed that there is a 2% fee charged for the balance transferred.
Note: The number of periods that is essential to pay back the loan with no fees is calculated first. The number of payments is solved using the formulae of the present value of
Formula to calculate the present value annuity:
Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period.
Compute the present value annuity for without fee:
Solving t with this equation:
Hence, the number of months without an annual fee at the rate of 18.60% is 113.94 months.
Note: Now the value of t is computed using the formulae of the present value of an annuity without fee and at an annual rate of 9.20%
Formula to calculate the present value annuity:
Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period.
Compute the present value annuity for without fee:
Solving t with this equation:
Hence, the number of months without an annual fee at the rate of 9.20% is 68.84 months.
Calculation of the months to pay off the new card without fee:
Note: The quicker months to pay off the card is calculated by subtracting the calculated number of months without an annual fee at 9.20% from the calculated number of months without an annual fee at 18.60%.
Hence, the faster payments made by Person X without a fee on the new card is 45.10 months
Note: It is not necessary to compute the time that is needed to pay back the current credit of Person X with a fee as it incurs no fee. It will take 113.94 months to pay off the current card of Person X.
Calculations of the time taken to pay back the new card with a transfer fee:
The calculations of the time taken to pay back the new card with a transfer fee are made with the help the equations of the present value of the annuity. The annual rate is 9.20%.
Formula to calculate the present value annuity:
Note: C denotes the payments, r denotes the rate of exchange, and t denotes the period.
Compute the present value annuity for without fee:
Note: The 2% interest rate is added to the present value of an annuity amount
Solving t with this equation:
Hence, the number of months with an annual fee at the rate of 9.20% is 70.66 months.
Calculation of the months to pay off the new card without a fee:
Hence, the faster payments made by Person X with a fee on the new card is 43.28 months.
Want to see more full solutions like this?
Chapter 6 Solutions
Fundamentals of Corporate Finance
- (Use Formula Approach or Calculator Approach) You ran a little short on your spring break vacation, so you put $1,000 on your credit card. You can afford only the minimum payment of $20 per month. The interest rate on the credit card is 1.5 percent per month. How long will you need to pay off the $1,000?arrow_forwardNonearrow_forward5.6 Just a Little Bit Each Month You've recently finished your MBA at the Darnit School. Naturally, you must purchase a new BMW immediately. The car costs about $42,000. The bank quotes an interest rate of 15 percent APR for a 72-month loan with a 10 percent down payment. What will your monthly payment be? What is the effective interest rate on the loan? (See Problem 20.)arrow_forward
- 2. Suppose you have a bank account into which you make $100 deposits each month. You find a bank account paying r 100% (r is a decimal rate) per month. You would like to save up for a $2,000 car down payment, which you would like to have in 15 months. What must the bank account pay in order for this to be accomplished?arrow_forwardYou ran a little short on your spring break vacation, so you put $1,000 on your other credit card. You can afford only the minimum payment of $60 per quarter. The interest rate on the credit card is 18 per year compounded quarterly. How many years will you need to pay off the $1,000? I want to solve this problem using the financial calculator so if your able to show me what to punch in that would be greatarrow_forwardNonearrow_forward
- Solve Problem 20.22 using Excel.arrow_forwardA K w an example Get more help. % Part 1 of 3 You are considering two ways of financing a spring break vacation. You could put it on your credit card, at 15% APR, compounded monthly, or borrow the money from your parents, who want an interest payment of 7% every six months. Which is the lower rate? (Note: Be careful not to round any intermediate steps less than six decimal places.) The effective annual rate for your credit card is 5 Search or enter website name 6 MacBook Pro Y & * BAAAABB 8 9 7 %. (Round to two decimal places.) Clear all U Save 0 Check answer XE Incorrec DADOS { I +arrow_forwardK You have just taken out a five-year loan from a bank to buy an engagement ring. The ring costs $5,500. You plan to put down $1,200 and borrow $4,300. You will need to make annual payments of $1,200 at the end of each year. Show the timeline of the loan from your perspective. How would the timeline differ if you created it from the bank's perspective? Show the timeline of the loan from your perspective. (Select the best choice below.) OA. Year Cash Flow $4,300 0 OB. Year 0 Cash Flow - $1,200 OC. Year Cash Flow $5,500 0 OD. Year 1 - $1,200 1 $1,200 2 Cash Flow - $4,300 $1,200 - $1,200 2 $1,200 - $1,200 - $1,200 2 $1,200 3 - $1,200 3 $1,200 3 - $1,200 3 $1,200 - $1,200 4 $1,200 4 - $1,200 4 $1,200 5 - $1,200 5 $1,200 5 - $1,200 5 $1,200arrow_forward
- NOTE that significant marks will be lost if your answer does not include the NUMERICAL FORMULA. Question 1 ( Time Value of Money and WACC) (a) You need to pay off a car loan within the next two years. The payment will be $4,000 every month. Today you have made a single deposit into a return-guaranteed investment account that will allow you to cope with all the monthly payments. This account earns an effective annual interest rate of 12.68250301%. The first payment will be made in one month. (i) Calculate the corresponding monthly rate for the investment account. (ii) “You need to have at least $96,000 at your account today in order to make all the payments on the car loan in the next two years.” True or false? Briefly explain without doing any time value of money related (i.e. PVA or FVA) calculations. (iii) What is the amount of the single deposit made today? (iv) If your mother is going to make the first year’s repayments for you (as a birthday gift) and thus you don’t…arrow_forwardplease answer fast i give upvotearrow_forwardsolve it correctly.not use excelarrow_forward
- Essentials Of InvestmentsFinanceISBN:9781260013924Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.Publisher:Mcgraw-hill Education,
- Foundations Of FinanceFinanceISBN:9780134897264Author:KEOWN, Arthur J., Martin, John D., PETTY, J. WilliamPublisher:Pearson,Fundamentals of Financial Management (MindTap Cou...FinanceISBN:9781337395250Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage LearningCorporate Finance (The Mcgraw-hill/Irwin Series i...FinanceISBN:9780077861759Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan ProfessorPublisher:McGraw-Hill Education