5-23. FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS Find the amount to which $500 will grow under each of these conditions: a. 12% compounded annually for 5 years b. 12% compounded semiannually for 5 years C. 12% compounded quarterly for 5 years d. 12% compounded monthly for 5 years e. 12% compounded daily for 5 years Why does the observed pattern of FVs occur?
5-24. PRESENT VALUE FOR VARIOUS DISCOUNTING PERIODS Find the present value of 5500 due in the future under each of these conditions: a. 12% nominal rate. semiannual compounding, discounted back 5 years Answer • b. 12% nominal rate, quarterly compounding discounted back 5 years Answer c. 12% nominal rate, monthly compounding, discounted back 1 year
d. Why do the differences in the PVs occur?
5-25. FUTURE VALUE OF AN ANNUITY Find the future values of the following ordinary annuities:
a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually
b. FV of $200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly
c. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?
5-26. PV AND LOAN ELIGIBILITY You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $350. The loan will have a 12% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? For 60 months?
5-34. AMORTIZATION SCHEDULE
a. Set up an amortization schedule for a $19,000 loan to be repaid in equal installments at the end of each of the next 3 years. The interest rate Is 8% compounded annually.
b. What percentage of the payment represents Interest and what percentage represents principal for each of the 3 years? Why do these percentages change over time?
5-35. AMORTIZATION SCHEDULE WITH A BALLOON PAYMENT You want to buy a house that costs $140.000. You have $14.000 for a down payment, but your credit is such that mortgage companies will not lend you the required $126,000. However, the realtor persuades the seller to take a $126,000 mortgage (called a seller take-back mortgage) at a rate of 5%, provided the loan Is paid off In full in 3 years. You expect to inherit $140.000 in 3 years, but right now all you have is $14,000, and you can afford to make payments of no more than $22,000 per year given your salary. (The loan would call for monthly payments, but assume end-of-year annual payments to simplify things.)
a. If the loan was amortized over 3 years, how large would each annual payment be? Could you afford those payments?
b. If the loan was amortized over 30 years, what would each payment be? Could you afford those payments?
c. To satisfy the seller, the 30-year mortgage loan would be written as a balloon note. which means that at the end of the third year, you would have to make the regular payment plus the remaining balance on the loan. What would the loan balance be at the end of Year 3, and what would the balloon payment be?
5-36. NONANNUAL COMPOUNDING
a. You plan to make five deposits of $1.000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 6% nominal interest, compounded semiannually, how much will be in your account after 3 years?
b. One year from today you must make a payment of $4,000. To prepare for this payment. you plan to make two equal quarterly deposits (at the end of Quarters 1 and 2) in a bank that pays 6% nominal interest compounded quarterly. How large must each of the two payments be?
5-37. PAYING OFF CREDIT CARDS Simon recently received a credit card with an 18% nominal interest rate. With the card, he purchased an Apple !Phone 11 for $700. The minimum payment on the card is S20 per month.
a. If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card?
b. If Simon makes monthly payments of S70, how many months will it be before he pays off the debt?
c. How much more in total payments will Simon make under the $20-a-month plan than tinder the $70-a-month plan? Make sure you use three decimal places for N.
5-38. PV AND A LAWSUIT SETTLEMENT It is now December 31, 2020 (t. = 0), and a Jury Just found in favor of a woman who sued the city for Injuries sustained in a January 2019 accident. She requested recovery of lost wages plus $300.000 for pain and suffering plus $60,000 for legal expenses. Her doctor testified that she has been unable to work since the accident and that she will not be able to work in the future. She is now 62, and the jury decided that she would have worked for another 3 years. She was scheduled to have earned 536,000 in 2019. (To simplify this problem, assume that the entire annual salary amount would have been received on December 31, 2019.) Her employer testified that she probably would have received raises of 3% per year. The actual payment for the jury award will be made on December 31, 2021. The judge stipulated that all dollar amounts are to be adjusted to a present value basis on December 31, 2021, using an 8% annual interest rate and using compound, not simple, interest. Furthermore, he stipulated that the pain and suffering and legal expenses should be based on a December 31, 2020. date. How large a check must the city write on December 31, 2021?
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