# Project #82693 - Sinking Funds, and Annuities, Using Financial Calculators

1)
Aunt Esmeralda promises to give her nephew \$35,000 on his 30th birthday, 14½ years from now. Aunt Esmeralda can earn 5.8% compounded semiannually. What amount could Aunt Esmeralda deposit today in a savings plan so that the plan would have the required \$35,000 in 14½ years?

 A \$15,453.46 B \$23,123.05 C \$6,823.13 D \$15,276.44

2)
Refer to Problem 1. If, instead, Aunt Esmeralda elects to make semiannual deposits into the plan (starting in 6 months), what is the required semiannual deposit?

 A \$1,604.92 B \$1,976.09 C \$786.15 D \$763.99

3)
Refer to Problems 1 and 2. If Aunt Esmeralda deposits \$5,000 today, what additional amount must she deposit at the end of each semiannual period?

 A \$1,085.64 B \$1,548.79 C \$14,819.76 D \$528.84

4)
While your doctor is taking your blood pressure, he is talking with his nurse about some new medical equipment he wants to buy in 3½ years for \$60,000. He wonders how much money he must deposit at the end of each month to accumulate \$60,000. You get his attention and tell him if he will listen for a moment you will help him calculate the amount. What amount is required if he can earn 7% compounded monthly?

 A \$1,428.57 B \$1,264.85 C \$1,663.71 D \$1,614.85

For Problems 5-7, help a Chinese auto manufacturer make calculations on some bonds. The company issues 935,000,000 yuan of 8% 15-year bonds to upgrade its assembly line. Terms of the bond require annual interest payments to bondholders plus annual deposits to a sinking fund for retirement of the bonds when they mature.

5)
How much interest must the corporation pay to the bondholders each year?

 A 74,800 yuan B 748,000 yuan C 7,480,000 yuan D 74,800,000 yuan

6)
Assuming the corporation can earn 9% compounded annually on its sinking fund, how much must it deposit into the fund at the end of each year?

 A 31,845,055.28 yuan B 34,435,642.52 yuan C 31,884,837.51 yuan D 29,215,647.04 yuan

7)
What is the total amount the corporation needs each year to meet its obligations on the bonds?

 A 106,645,055.28 yuan B 104,015,647.04 yuan C 109,235,642.52 yuan D 106,684,837.51 yuan

8)
Kyle just turned 24 and can save \$200 per month, starting in 1 month. If Kyle can earn 5.25% compounded monthly, what age will he be when he accumulates \$1,000,000?

 A 717 years old B 741 years old C 59 years old D 83 years old

Unit 13.2 Annuities

For Problems 9-14, pretend you receive an inheritance of \$650,000 and deposit it in a savings plan that earns 5.25% compounded monthly.

9)
If you want to live off the interest without withdrawing any of the \$650,000 principal, what amount can you withdraw at the end of each month?

 A \$34,125 B \$409,500 C \$3,412.50 D \$2,843.75

10)
How much can you withdraw at the end of each month if you want the plan to last 35 years?

 A \$3,384.83 B \$40,957.13 C \$1,547.62 D \$3,370.09

11)
How much can you withdraw at the end of each month if you want the plan to last 50 years?

 A \$1,083.33 B \$2,843.75 C \$3,927.08 D \$3,067.21

12)
If you withdraw \$4,550 at the end of each month, how long will the plan last?

 A 142.86 months B 224.68 months C 193.77 months D 193.86 months

13)
If you withdraw less than the amount you calculated in Problem 9, the balance will increase. (T or F)

 A True B False

14)
If you withdraw \$2,800 at the end of each month, what will the balance be in 30 years?

 A \$5,570,285.83 B \$3,211,224.27 C \$688,141.75 D 2,822,792.15

15)
A wealthy citizen sets up a trust for scholarships at a local community college. The gift is for \$3,500,000 and the money is to be distributed at the beginning of each year over the next 200 years. If the trust earns 5.25% compounded annually, how much is available for scholarships each year?

 A \$174,590.60 B \$183,756.60 C \$183,750 D \$201,250

Unit 13.3 Loan payments

16)
You are thinking about buying a hot tub priced at \$24,999. Your bank will loan you \$20,500 at 7.7% for 5 years. Determine your monthly payment

 A \$6,211.73 B \$5,093.83 C \$412.73 D \$503.31

17)
Refer to Problem 16. What is the total amount of interest you will pay over the 5 years?

 A \$6,059.65 B \$4,969.15 C \$4,263.80 D \$5,199.60

18)
If you purchase an iPod for \$1,900 and the store finances the entire amount over 36 months at a monthly rate of 1.45%, what is your monthly payment?

 A \$68.12 B \$53.97 C \$52.78 D \$54.18

For Problems 19-22, assume you need a \$180,000 mortgage loan but are unsure whether to get a 7.5% 15-year loan or a 7.75% 30-year loan.

19)
Calculate the monthly payment for the 15-year loan.

 A \$1,668.62 B \$1,258.59 C \$1,289.54 D \$1,694.30

20)
Calculate the monthly payment for the 30-year loan.

 A \$1,668.62 B \$1,258.59 C \$1,289.54 D \$1,694.30

21)
Find the total amount of interest for the 15-year loan.

 A \$300,351.60 B \$464,234.40 C \$120,351.60 D \$284,234.40

22)
Find the total amount of interest for the 30-year loan.

 A \$300,351.60 B \$464,234.40 C \$120,351.60 D \$284,234.40

23)
Calculate the monthly payment on a 25-year \$450,000 mortgage loan at 6 7/8% interest.

 A \$3,117.63 B \$30,510.00 C \$3,146.14 D \$3,144.71

24)
Several years ago you got a mortgage loan at 6.75% interest. You currently owe \$56,414.83 with a monthly payment of \$667.55. How long until the loan will be paid off?

 A 69.33 months B 29.13 months C 115.00 months D Solution not possible

25)
Refer to Problem 24. How many months will it take until the loan will be paid off if you pay an extra \$70 each month?

 A 164.09 months B 100.29 months C 63.80 months D Solution not possible

Challenge problems

26)
You serve on the board of directors for a yacht club. The docks must be refurbished in 3 years. The cost of refurbishing today is \$750,000, and the cost is estimated to increase at an annual rate of 4.5%. What will the cost be in 3 years?

 A \$783,750 B \$851,250 C \$855,874.59 D \$851,650.59

27)
Refer to Problem 26. What amount must be deposited into a sinking fund at the end of each month to accumulate the amount needed if the fund earns 6.75% compounded monthly?

 A \$19,701.85 B \$21,398.66 C \$21,408.73 D \$21,514.91

28)
Calculate the term for a 9.5% \$2,000 loan with monthly payments of \$25.

 A 127.23 months B 23.71 months C 80.00 months D 124.71 months

29)
Refer to Problem 28. Calculate the term with monthly payments of \$50.

 A 34.89 months B 48.29 months C 17.28 months D 63.62 months

30)
Refer to Problems 28 and 29. By doubling the monthly payment, you exactly halve the term. (T or F)

 A True B False

31)
You have just made your \$326.98 monthly payment on your 10.5% car loan. Your balance, after the payment, is \$8,967.33. How many months will it take to pay off the loan?

 A 13.58 months B 24.69 months C 27.42 months D 31.50 months

32)
Refer to Problem 31. You just received an income tax refund of \$1,330. If you apply the refund as an extra principal payment immediately after making the above monthly payment, how many monthly payments will you save?

 A 26.24 months B 21.35 months C 12.41 months D 5.26 months

33)
You see a truck advertisement, showing the dealer will give the buyer either (1) a \$2,500 cash rebate, or (2) 3.0% financing for 5 years. The dealer’s price (before rebate) is \$18,999, and the current interest rate of 5-year truck loans is 8.75%. Calculate a monthly payment for each choice, assuming that you use the cash rebate to reduce the loan amount. What is the monthly payment for each choice?

 A \$352.47 for Choice 1 and \$358.44 for Choice 2 B \$340.49 for Choice 1 and \$341.39 for Choice 2 C \$340.49 for Choice 1 and \$358.44 for Choice 2 D \$352.47 for Choice 1 and \$341.39 for Choice 2

34)
You can afford a monthly mortgage payment of \$1,250 and can get a 30-year 7% loan. What is the maximum loan you can get so your payment does not exceed \$1,250?

 A \$15,511.30 B \$187,884.46 C \$17,857.14 D \$181,455.05

35)
Ping Johnston is 32 years old. Some of Ping’s older relatives have retired, having no income other than Social Security. Ping does not want to be caught in that situation, so she is thinking about setting up a retirement plan. Ping wants to retire at age 55, 23 years from now, and wants her retirement plan to provide \$2,500 a month for 40 years (until she is 95). Her plan can earn 6.8% compounded monthly. What amount must Ping deposit at the end of each month for the next 23 years so that she can then start receiving \$2,500 at the end of each month for the following 40 years?

 A \$593.88 B \$647.12 C \$610.88 D \$621.28

36)
Refer to Problem 35. How much interest will Ping’s retirement plan earn over the 63 years?

 A \$1,021,394.88 B \$1,031,397.12 C \$1,036,089.12 D \$1,028,526.72

37)
In 14 years, Carlos Rodriquez’s daughter will be entering college and Carlos would like to help financially. Tuition is currently \$7,335 a year, but is expected to increase at a rate of 3.5%, compounded annually. Carlos decides to create a college fund and make 14 annual deposits, starting in one year. In 14 years, he would like his daughter to be able to make 4 annual withdrawals from the fund (at the beginning of each year) that will cover her annual tuition. If the college fund earns 5.55% compounded annually, how much must Carlos deposit at the end of each year? Note : Assume that tuition will remain the same for the 4 years of college

 A \$2,178.29 B \$2,154.65 C \$2,202.88 D \$2,139.88

 Subject Mathematics Due By (Pacific Time) 09/22/2015 12:00 am
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