# Math Chapter 6

\$10,000 is invested for 6 years at an annual simple interest rate of 16%.
a. How much interest will be earned?
b. What is the future value of the investment at the end of the 6 years?
6.1-5
a. 9,600
b. 19,600
\$1,000 is invested for 3 months at an annual simple interest rate of 12%
a. How much interest will be earned?
b. What is the future value of the investment after 3 months?
6.1-7

a. 30
b. 1,030

If you borrow \$1,600 for 2 years at 14% annual simple interest, how much must you repay at the end of the 2 years?
6.1-10

2,048

If you lend \$3,500 to a friend for 15 months at 8% annual simple interest, find the future value of the loan
6.1-11

3,850

a. To buy a treasury bill that matures to \$10,000 in 6 months, you must pay \$9,750. What rate does this earn?
b. If the bank charges a fee of \$40 to buy a T-bill, what is the actual interest rate you earn?
6.1-15

a. 5.13%
b. 4.29%

A firm buys 12 file cabinets at \$140 each, with the bill due in 90 days. How much must the firm deposit now to have enough to pay the bill if money is worth 12% per year?
Use 360 days in a year
6.1-17

1,631.07

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A student has a savings account earning 9% simple interest. She must pay \$1,500 for first semester tuition by Sept 1 and \$1,500 for second semester tuition by Jan 1. How much must she earn in the summer (by Sept) in order to pay the first semester bill on time and still have the remainder of her summer earnings grow to \$1,500 between Sept 1 and Jan 1?
6.1 -18

2,956.31

If you want to earn 15% annual simple interest on an investment, how much should you pay for a note that will be worth \$13,500 in 10 months?
6.1-19

12,000

What interest will be earned if \$6,300 if invested for 3 years at 12% compounded monthly?
6.2-12

2,713.84

What lump sum do parents need to deposit in an account earning 10%, compounded monthly, so that it will grow to \$80,000, for their son’s college tuition in 18 years?
6.2-13

13,322.91

What present value amounts to \$10,000 if it is invested for 10 years at 6% compounded annually?
6.2 – 15

5,583.95

Find the future value if \$5,100 is invested for 4 years at 9% compounded continuously
6.2-17

7,309.98

What is the compound interest if \$410 is invested for 10 years at 8% compounded continuously?
6.2-19

502.47

Grandparents want to make a gift of \$100,000 for their grandchild’s 20th birthday. How much would have to be invested on the day of their grandchild’s birth if their investment could earn
a. 10.5% compounded continuously
b. 11% compounded continuously
c. Describe the effect that this slight change in the interest rate makes over the 20 years of this investment
6.2 – 21

a. 12,245.64
b. 11,080.32
c. 1,165.32

How much more interest will be earned if \$5,000 is invested for 6 years at 7% compounded continuously, instead of at 7% compounded quarterly?
6.2 – 24

27.60

Find the annual percentage yield for an investment at
a. 7.3% compounded monthly
b. 6% compounded continuously
6.2 – 25

a. 7.55%
b. 6.18%

Two different companies offer college savings plans, one at 8.2% compounded continuously and the other at 8.4% compounded quarterly. Which is the better investment?
6.2-29

8.67 or 8.55

8.67 better investment

The figure shows a graph of the future value of \$100 at 8% compounded annually, along with the graph of \$100 at 8% compounded continuously. Which is which? Explain
6.2 – 31

S = 100(1.08)^t
S = 100e^.08t

The higher graph is for continuous compounding because its yield is higher

Microsoft’s stock price peaked at 6118% of its IPO price more than 13 years after the IPO. Suppose that \$10,000 invested in Microsoft at its IPO price had been worth \$600,000 (6000% of the IPO price) after exactly 13 years. What interest rate, compounded annually, does this represent?
6.2 – 33

37.02%

How long (in years) would \$700 have to be invested at 11.9% compounded continuously, to earn \$300 interest?
6.2-35

Approx 3 years

A couple needs \$15,000 as a down payment for a home. If they invest the \$10,000 they have at 8% compounded quarterly, how long will it take for the money to grow into \$15,000?
6.2-43

5.1188

A house that 20 years ago was worth \$160,000 has increased in value by 4% each year because of inflation. What is its worth today?
6.2-61

350,579.70

A machine is valued at \$10,000. If the depreciation at the end of each year is 20% of its value at the beginning of the year, find its value at the end of 4 years?
6.2-69

4,096

If changing market conditions cause a company earning \$8,000,000 in 2005 to project a loss of 2% of its profit in each of the next 5 years, what profit does it project in 2010?
6.2-73

7,231,366.37

Find the future value of an annuity of \$1,300 paid at the end of each year for 5 years, if interest is earned at a rate of 6% compounded annually
6.3-7

7,328.22

Find the future value of an ordinary annuity of \$80 paid quarterly for 3 years, if the interest rate if 8% compounded quarterly
6.3-9

1,072.97

A sinking fund is established to discharge a debt of \$80,000 in 10 years. If deposits are made at the end of each 6 month period and interest is paid at the rate of 8% compounded semiannually, what is the amount of each deposit?
6.3 – 12
2,686.54
If \$2,500 is deposited at the end of each quarter in an account that earns 5% compounded quarterly, after how many quarters will the account contain \$80,000?
6.3 – 13

28 months

Find the future value of an annuity due of \$1,500 each month for 3 years if the interest rate is 12% compounded monthly
6.3 – 20

65,261.47

How much must be deposited at the beginning of each year in an account that pays 8%, compounded annually, so that the account will contain \$24,000 at the end of 5 years?
6.3 – 23

3,787.92

A family wants to have a \$200,000 college fund for their children at the end of 20 years. What contribution must be made at the end of each quarter if their investment pays 7.6% compounded quarterly?
6.3 – 29

1,083.40

Mr. Gordon plans to invest \$300 at the end of each month in an account that pays 9%, compounded monthly. After how many months will the account be worth \$50,000?
6.3 – 33

109 months

How much money should a couple deposit at the end of each month in an investment plan that pays 7.5% compounded monthly, so they will have \$800,000 in 30 years?
6.3 – 36

593.72

Jane Adele deposits \$500 in an account at the beginning of each 3 month period for 9 years. If the account pays interest at the rate of 8%, compounded quarterly, how much will she have in her account after 9 years?
6.3 – 37

26,517.13

Suppose a recent college graduate’s first job allows her to deposit \$100 at the end of each month in a savings plan that earns 9% compounded monthly. This savings plan continues for 8 years before new obligations make it impossible to continue. If the accrued amount remains in the plan for the next 15 years without deposits or withdrawals, how much money will be in the account 23 years after the plan began?
6.3 – 41

53,677.38

Find the present value of an annuity of \$6,000 paid at the end of each month 6 month period for 8 years if the interest rate if 8%, compounded semiannually.
6.4 – 5

69,913.77

Suppose a state lottery prize of \$5 million is to be paid in 20 payments of \$250,000 each at the end of each of the next 20 years. If money is worth 10% compounded annually, what is the present value of the prize?
6.4 – 7

2,128,390.93

With a present value of \$135,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 6.4% compounded quarterly?
6.4 – 9

4,595.46

If \$88,000 is invested in an annuity that earns 5.8% compounded quarterly, what payments will it provide at the end of each quarter for the next 5.5 years?
6.4 – 10

4,700.55

Find the present value of an annuity due that pays \$3,000 at the beginning of each quarter for the next 7 years. Assume that money is worth 5.8% compounded quarterly
6.4 – 19

69,632.02

What amount must be set aside now to generate payments of \$50,000 at the beginning of each year for the next 12 years if money is worth 5.92% compounded annually?
6.4 – 21

445,962.23

A year-end bonus of \$25,000 will generate how much money at the beginning of each month for the next year, if it can be invested at 6.48%, compounded monthly?
6.4 – 23

2,145.59

Is it more economical to buy an automobile for \$29,000 cash or to pay \$8,000 down and \$3,000 at the end of each quarter for 2 years, if money is worth 8% compounded quarterly?
6.4 – 28

29,978.44

Recent sales of some real estate and record profits make it possible for a manufacturer to set aside \$800,000 in a fund to be used for modernization and remodeling. How much can be withdrawn from this fund at the beginning of each half-year for the next 3 years if the fund earns 7.7% compounded semiannually?
6.4 – 31

146,235.06

On his 48th birthday, a man wants to set aside enough money to provide an income of \$1,500 at the end of each month from his 60th birthday to his 65th birthday. If he earns 6% compounded monthly, how much will this supplemental retirement plan cost him on his 48th birthday?
6.4 – 48

37,834.11

Danny Metzger’s parents invested \$1,600 when he was born. This money is to be used for Danny’s college education and is to be withdrawn in four equal annual payments beginning when Danny is age 19. Find the amount that will be available each year, if money is worth 6% compounded annually.
6.4 – 51

1,317.98

A couple received a \$134,000 inheritance the year they turned 48 and invested it in a fund that earns 7.7% compounded semiannually. If this amount is deferred for 14 years, how much will it provide at the end of each half-year for the next 20 years after they retire?
6.4 – 54

19,064.49

A debt of \$8,000 is to be amortized with 8 equal semiannual payments. If the interest rate is 12%, compounded semiannually, what is the size of each payment?
6.5 – 3

1,288.29