1) Recently, Jamie and Jake each bought new cars. Both received a loan from a lo

Question

1) Recently, Jamie and Jake each bought new cars. Both received a loan from a local bank with a nominal interest rate of 12% where payments are made at the end of each month, and they both pay the same monthly payment. Jamie's loan is for $15,000; however, his loan matures at the end of 4 years (48 months), while Jake's loan matures in 5 years (60 months). After 48 months Jamie's loan will be paid off, but what will be the remaining balance on Jake's loan

2) Karen and her twin sister, Kathy, are celebrating their 30th birthday today. Karen has been saving for her retirement ever since their 25th birthday. On their 25th birthday, she made a $5,000 contribution to her retirement account. Every year thereafter on their birthday, she has added another $5,000 to the account. Her plan is to continue contributing $5,000 every year on their birthday. Her 41st, and final, $5,000 contribution will occur on their 65th birthday. So far, Kathy has not saved anything for her retirement but she wants to begin today. Kathy’s plan is to also contribute a fixed amount every year. Her first contribution will occur today, and her 36th, and final, contribution will occur on their 65th birthday. Assume that both investment accounts earn an annual return of 10 percent. How large does Kathy’s annual contribution have to be for her to have the same amount in her account at age 65, as Karen will have in her account at age 65?

3) What is the future value of an annuity of $150 per year (first cash flow occurs one year from today) for 43 years if the interest rate is 11% p.a.?

4) What is the future value exactly 29 years from today of a deposit of $4,832 made today into an account that pays interest of 10% p.a.?

5)If the price of a loaf of bread has tripled over the past 7 years, what has been the annual rate of inflation in the price of bread over that time period?

6)You are about to deposit $580 into one of the following savings accounts to be left on deposit for 25 years. Each bank offers an account with a different interest rate and compounding period. Assuming you want to maximize your wealth, how much money would be in the bank account that offers the best effective rate of return after 25 years?

BANK A: 9.5 percent rate compounded semi-annually
BANK B: 9.4 percent rate compounded monthly
BANK C: 9.3 percent rate compounded daily
BANK D: 9.2 percent rate compounded continuously

(Enter the amount only - do not enter the bank letter. Round your answer to 2 decimal places and record your answer without a dollar sign and without commas)

7) What is the present value of 63 annual payments of $1,075 each with the first payment being received immediately? Assume you can invest money at a 10% stated rate with semi-annual compounding.

8) John Keene recently invested $2,250 in a project that is promising to return 10 percent per year. The cash flows are expected to be as follows:

           End of                                       Cash
               Year                                           Flow
               1                                     $540
               2                                     $506
               3                                     $558
               4                                      ??
               5                                     $546

Note that the cash flow in year 4 is missing. Determine the Year 4 missing cash flow that will make the present value of this series equal to the amount John invested (that is, $2,250)? (Round your answer to 2 decimal places and record your answer without a dollar sign and without commas).

9) Your bank offers 3-year certificates of deposit with a stated rate of interest of 11.47% p.a., compounded quarterly. Your cousin (who works at Acme Bank and Trust, a competitor) wants to know what stated rate of interest you would require from them in order to switch your business to their bank. Acme's CD's are compounded on a monthly basis. What is the minimum stated interest rate you should ask for from Acme in order to make you indifferent to switching?

10) Assume that exactly three years ago I borrowed $417,000. My loan has an interest rate of 4.25% and the term of the loan is 30 years (with required payments to be made every month). If I made every required payment on time for the first 36 months of the loan, what is my current payoff on my loan (that is, immediately after making my 36th payment)?

11)Assume that the e-trade baby opened an investment account when he turned 2 (i.e., he made his first deposit into the account on his second birthday). His deposit on that day was for $50,000 (this was his royalty check from one of his commericials). Assume that he continued making deposits into the account every month (his first monthly deposit was exactly one month after he made his initial $50,000 deposit) for the next 35 months (thus, his last deposit is made on this 5th birthday). The amount of these monthly deposits was $2500 per month. If the interest rate that he earns on his account is 6.5% p.a., but with monthly compounding, how much money will be in his account when he turns 55 years old (that is, exactly 50 years after he makes his last monthly deposit into the account)

Explanation / Answer

A) Calculation for jamie's monthly payment:

Jakes monthly payment = jamies monthly payment = 395

Using this for 60 month period

At end of 48 month period balance remaining = 4445.84

B)

K = N          
Present value of Karens' contribution= [(contribution)/(1 + YTM)^k]   
k=1

                    K = 41   
= [(5000)/(1 + 10/100)^k]
                   k=1

   = 48995.65

This should be equal to kathy's PV of contribution

   K = (65-36)
48995.65 = [(Contribution)/(1 + 10/100)^k]
k=1

Kathys' contribution should be 5229.215

C)

C = Cash flow per period

i = interest rate

n = number of payments

FV = 150 *[((1+ 11/100)^43 -1)/(11/100)] = 119859.819

D) FV = PV * (1 + r)^n = 4832 * ( 1 + 0.1) ^ 29 = 76650.465

Please ask remaining questions separately

Monthly rate(M)= annual rate/12= 1.00% Monthly payment= 395.0075315 Month Beginning balance (A) Monthly payment Interest = M*A Principal paid Ending balance 1 15000 395.0075315 150 245.0075315 14754.99247 2 14754.99247 395.0075315 147.5499247 247.4576068 14507.53486 3 14507.53486 395.0075315 145.0753486 249.9321829 14257.60268 4 14257.60268 395.0075315 142.5760268 252.4315047 14005.17117 5 14005.17117 395.0075315 140.0517117 254.9558197 13750.21535 6 13750.21535 395.0075315 137.5021535 257.5053779 13492.70998 7 13492.70998 395.0075315 134.9270998 260.0804317 13232.62954 8 13232.62954 395.0075315 132.3262954 262.681236 12969.94831 9 12969.94831 395.0075315 129.6994831 265.3080484 12704.64026 10 12704.64026 395.0075315 127.0464026 267.9611289 12436.67913 11 12436.67913 395.0075315 124.3667913 270.6407402 12166.03839 12 12166.03839 395.0075315 121.6603839 273.3471476 11892.69124 13 11892.69124 395.0075315 118.9269124 276.080619 11616.61062 14 11616.61062 395.0075315 116.1661062 278.8414252 11337.7692 15 11337.7692 395.0075315 113.377692 281.6298395 11056.13936 16 11056.13936 395.0075315 110.5613936 284.4461379 10771.69322 17 10771.69322 395.0075315 107.7169322 287.2905993 10484.40262 18 10484.40262 395.0075315 104.8440262 290.1635053 10194.23912 19 10194.23912 395.0075315 101.9423912 293.0651403 9901.173977 20 9901.173977 395.0075315 99.01173977 295.9957917 9605.178186 21 9605.178186 395.0075315 96.05178186 298.9557496 9306.222436 22 9306.222436 395.0075315 93.06222436 301.9453071 9004.277129 23 9004.277129 395.0075315 90.04277129 304.9647602 8699.312369 24 8699.312369 395.0075315 86.99312369 308.0144078 8391.297961 25 8391.297961 395.0075315 83.91297961 311.0945519 8080.203409 26 8080.203409 395.0075315 80.80203409 314.2054974 7765.997912 27 7765.997912 395.0075315 77.65997912 317.3475524 7448.650359 28 7448.650359 395.0075315 74.48650359 320.5210279 7128.129331 29 7128.129331 395.0075315 71.28129331 323.7262382 6804.403093 30 6804.403093 395.0075315 68.04403093 326.9635005 6477.439593 31 6477.439593 395.0075315 64.77439593 330.2331356 6147.206457 32 6147.206457 395.0075315 61.47206457 333.5354669 5813.67099 33 5813.67099 395.0075315 58.1367099 336.8708216 5476.800169 34 5476.800169 395.0075315 54.76800169 340.2395298 5136.560639 35 5136.560639 395.0075315 51.36560639 343.6419251 4792.918714 36 4792.918714 395.0075315 47.92918714 347.0783443 4445.840369 37 4445.840369 395.0075315 44.45840369 350.5491278 4095.291242 38 4095.291242 395.0075315 40.95291242 354.0546191 3741.236623 39 3741.236623 395.0075315 37.41236623 357.5951653 3383.641457 40 3383.641457 395.0075315 33.83641457 361.1711169 3022.47034 41 3022.47034 395.0075315 30.2247034 364.7828281 2657.687512 42 2657.687512 395.0075315 26.57687512 368.4306564 2289.256856 43 2289.256856 395.0075315 22.89256856 372.1149629 1917.141893 44 1917.141893 395.0075315 19.17141893 375.8361125 1541.305781 45 1541.305781 395.0075315 15.41305781 379.5944737 1161.711307 46 1161.711307 395.0075315 11.61711307 383.3904184 778.3208884 47 778.3208884 395.0075315 7.783208884 387.2243226 391.0965658 48 391.0965658 395.0075315 3.910965658 391.0965658 -9.09495E-13

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