Deck 6: Mathematics of Finance

Question 1

If an initial investment of $3000 grows to $18,000 in ten years,find the nominal rate of interest,compounded monthly,that was earned by the money.

Answer 1

18.052%

Question 2

An interest rate of 8% compounded semiannually corresponds to an effective rate of

A) 8%.
B) 8.1600%.
C) 8.2031%.
D) 9.2456%.
E) 12%.

Answer 2

8.1600%.

Question 3

Suppose you leave an initial amount of $315 in a savings account for 10 years.If interest is compounded monthly,use a graphing calculator to graph the compound amount S as a function of the nominal rate of interest.Determine the nominal rate of interest so that there is $519 after 10 years.

Answer 3

5%

Question 4

At what nominal rate of interest,compounded semiannually,will an investment double in 20 years?

Question 5

A trust fund is to be established by a single payment so that at the end of 15 years,there will be $20,000 in the fund.If the fund earns interest at the rate of 8% compounded semiannually,how much should be deposited initially into the fund?

A) $6166.38
B) $6472.42
C) $7014.27
D) $7143.56
E) $11,105.30

Question 6

At what nominal rate of interest,compounded monthly,will an investment double in 15 years?

Question 7

To what sum will $1000 accumulate if it is invested at 10% compounded annually for one year and then at 10% compounded semiannually for two years?

Question 8

How many years will it take for a principal to double at a rate of 10% compounded annually? Give your answer to the nearest year.

Question 9

Suppose you leave an initial amount of $320 in a savings account for 30 years.If interest is compounded monthly,use a graphing calculator to graph the compound amount S as a function of the nominal rate of interest.Determine the nominal rate of interest so that the amount triples after 30 years.

Question 10

If an initial investment of $4000 grows to $4884 in five years,find the nominal rate of interest,compounded monthly,that was earned by the money.

Question 11

An initial investment of $2600 grows at an annual rate of 7.5% compounded monthly.Find how long it takes for the investment to amount to $3500.

Question 12

At what nominal rate of interest,compounded quarterly,will an investment double in 15 years?

Question 13

Find the effective rate that corresponds to an interest rate of 5% compounded daily.

Question 14

Suppose you leave an initial amount of $250 in a savings account for 20 years.If interest is compounded daily (use 365 times per year),use a graphing calculator to graph the compound amount S as a function of the nominal rate of interest.Determine the nominal rate of interest so that the amount doubles after 20 years.

Question 15

At what nominal rate of interest,compounded quarterly,will money double in 10 years?

Question 16

If an initial investment of $3000 grows to $18,000 in five years,find the nominal rate of interest,compounded quarterly,that was earned by the money.

Question 17

Over a period of 3 years,an original principal of $1000 accumulated to $1200 in an account where the interest rate was compounded monthly.Determine the rate of interest to two decimal places.

Question 18

What is the effective rate that corresponds to a nominal rate of 20% compounded quarterly?

Question 19

At what nominal rate of interest,compounded monthly,will an investment triple in 20 years?

Question 20

If an initial investment of $4000 grows to $5718 in six years,find the nominal rate of interest,compounded quarterly,that was earned by the money.

Question 21

Suppose you invest an initial amount of $10,000 at an annual rate of 8.2% compounded monthly.Use a graphing calculator to graph the compound amount S as a function of the interest periods.Determine how long it takes for the investment to accumulate to $22,500.

Question 22

You have a choice of two banks.One bank pays interest at 4.66% compounded 360 times a year and the other bank pays interest at 4.65% compounded 365 times a year.Which is the better choice?

Question 23

An investment grows from $600 to $642 in one year.If the investment continues to grow at that rate,find the number of years it will take for the investment to double.

Question 24

Suppose an initial investment grows from $220 to $600 over fifteen years.First find the nominal rate compounded monthly and then find the equivalent effective rate.

Question 25

Suppose an initial investment grows from $2000 to $2817.39 over three years.First find the nominal rate compounded monthly and then find the equivalent effective rate.

Question 26

The population of a small town is growing at an effective rate of 2.1%.If the current population is 53,000,what will the population be in 8 years?

Question 27

An investment grows from $5500 to $6105 in one year.If the investment continues to grow at that rate,find the number of years it will take for the investment to triple.

Question 28

Suppose an initial investment grows from $12,000 to $30,000 over ten years.First find the nominal rate compounded quarterly and then find the equivalent effective rate.

Question 29

Suppose you can invest $10,000 at 4.5% compounded quarterly or at 4.7% compounded annually.Which is the better choice and how much more per year would you earn?

Question 30

A house worth $150,000 ten years ago has increased in value at an effective rate of 3% due to inflation.Find the current value of the home.

Question 31

A $6000 investment in a stock five years ago grew at an effective rate of 19.6%.Find the current value of the investment.

Question 32

An investment is growing at an effective rate of 12.4%.If the amount invested is currently $12,000,what will the amount be in 6 years?

Question 33

The population of a city grows from 110,000 to 116,600 in one year.If the city continues to grow at that rate,find the number of years it will take for the population to double.

Question 34

An investment grows from $10,240 to $10,700.80 in one year.If the investment continues to grow at that rate,find the number of years it will take the investment to double.

Question 35

Suppose an initial investment grows from $330 to $600 over five years.First find the nominal rate compounded monthly and then find the equivalent effective rate.

Question 36

An initial investment of $300 grows at an annual rate of 4.5% compounded bimonthly.Find how long it takes for the investment to amount to $450.

Question 37

An investment is compounded daily (use 365 times per year).Use a graphing calculator to graph the effective rate,
,as a function of the nominal rate r.Then use the graph to find the nominal rate that is equivalent to an effective rate of 5.4%.

Question 38

Suppose you can invest $6000 at 6.2% compounded monthly or at 6.5% compounded semiannually.Which is the better choice and how much more per year would you earn?

Question 39

An initial investment of $10,000 grows at an annual rate of 3.5% compounded monthly.Find how long it takes for the investment to amount to $14,400.

Question 40

An initial investment of $240 grows at an annual rate of 5% compounded quarterly.Find how long it takes for the investment to amount to $300.

Question 41

A debt of $2000 due four years from now is to be repaid by a payment of $1000 now and a second payment at the end of two years.How much should the second payment be if the interest rate is 5% compounded annually?

Question 42

A debt of $2000 due in one year is to be repaid by a payment due two years from now and a final payment of $1000 three years from now.If the interest is at the rate of 4% compounded annually,then the payment due in two years is

A) $1000.00.
B) $1118.46.
C) $1155.43.
D) $1191.00.
E) $1203.14.

Question 43

If $4,200 is invested at an annual rate of 5.4% compounded monthly for 10 years,find the compound amount.

Question 44

If $5,600 is invested at an effective rate of 2.1% for 17 years,what is the compound amount?

Question 45

If $2,575 is invested at an A.P.R.of 7% compounded semiannually for 15 years,find the accumulated amount.

Question 46

If $10,000 is invested at an effective rate of 4.25% for 8 years,what is the accumulated amount?

Question 47

Find the present value of $300 due after six years if the interest rate is 5.4% compounded monthly.

Question 48

A bank pays 4% annual interest compounded quarterly.How large a deposit must be made now in order that the account contains $1500 at the end of 3 years?

Question 49

To purchase land for an industrial site,a company agrees to pay $20,000 down and $10,000 at the end of every six-month period for 10 years.If the interest rate is 10% compounded semiannually,what is the corresponding cash value of the land?

Question 50

For an initial investment of $10,000,suppose a company guarantees the following cash flows at the end of the indicated years:
Year Cash Flow
1 $4000
3 $8000
Assume an interest rate of 5% compounded annually.(a)Determine the net present value of the cash flows.(b)Is the investment profitable?

Question 51

If $14,300 is invested at an A.P.R.of 8.25% compounded semiannually for 3 years,find a)the compound amount,and b)the compound interest.

Question 52

Find the present value of $5000 due in 3 years if the interest rate is
% compounded monthly.

Question 53

Find the present value of $3000 due after five years if the interest rate is 9.6% compounded semiannually.

Question 54

A bank charges 0.5 % service fee on checking accounts.If $ 1,000 was deposited in such account,use the concept of negative interest rate to find an approximate value of the amount in this account after 10 years.

Question 55

A person has the option of satisfying a debt by either paying $5000 now and $5000 in two years,or by paying $3000 now,$3000 a year from now,and a final payment of x dollars two years from now.Determine an equation of value that corresponds to the value of all payments at the end of two years.It is not necessary to solve the equation.Assume that interest is at the rate of 10% compounded semiannually.

Question 56

You have a choice of two banks.One bank pays interest at 5.54% compounded monthly and the other bank pays interest at 5.53% compounded daily (365 times a year).Which is the better choice? How much more would you make in one year if you deposited $1000?

Question 57

If $3,100 is invested at a nominal rate of 6% compounded quarterly for 7 years,find a)the compound amount,and b)the compound interest.

Question 58

You have two investment opportunities.You can invest $6000 at 12% compounded monthly or you can invest $6100 at 12.1% compounded quarterly.Which has the better effective rate of interest? Use a graphing calculator to graph both amounts as a function of time in years.Which is the better investment over twenty years?

Question 59

Determine the present value of $4000 due in 5 years if the interest rate is 10% compounded semiannually.

Question 60

If $1,000 is invested at a nominal rate of 4% compounded quarterly for 5 years,find the compound amount.

Question 61

Suppose you have the opportunity to invest $1000 in a business such that the value of your investment after seven years will be $1500.On the other hand,you can put the $1000 into a certificate of deposit that pays 6% compounded monthly.Which is better?

Question 62

A debt of $1000 due 4 years from now and $1500 due 6 years from now,is instead to be paid off by a single payment 5 years from now.How much is the payment if an interest rate of 8.4% compounded monthly is assumed?

Question 63

A trust fund for a 8-year-old child is being set up by a single payment so that when the child is 20 there will be $12,000.If the fund earns interest at the rate of 6.5% compounded semiannually,how much money should be paid into the fund initially?

Question 64

Suppose that you can invest $10,000 in a business that guarantees you the following cash flows: $5000 at the end of 2 years,$4000 at the end of 4 years,and $3000 at the end of 6 years.Assuming an interest rate of 7.25% compounded annually,find the net present value of the cash flows.Is the investment profitable?

Question 65

Suppose that you can invest $8000 in a business that guarantees you the following cash flows: $4000 at the end of 2 years,$3500 at the end of 4 years,and $2000 at the end of 7 years.Use a graphing calculator to graph the net present value as a function of the interest rate compounded annually.Determine the interest rates for which the investment is profitable.

Question 66

Suppose that you can invest $5000 in a business that guarantees you the following cash flows: $3000 at the end of 2 years,$2000 at the end of 4 years,and $2000 at the end of 6 years.Assuming an interest rate of 6% compounded monthly,find the present value of the cash flows.Is the investment profitable?

Question 67

A trust fund for a newborn is being set up by a single payment so that at the end of 18 years there will be $34,000.If the fund earns interest at the rate of 6.25% compounded monthly,how much money should be paid into the fund initially?

Question 68

A debt of $600 is due 3 years from now and $800 due 5 years from now,is instead to be paid off by two payments: $500 now and a final payment at the end of 6 years.What would this payment be if an interest rate of 6% compounded quarterly is assumed?

Question 69

How much must be invested at an interest rate of 7.25% compounded quarterly to have $10,000 in two years?

Question 70

Suppose that you can invest $5000 in a business that guarantees you the following cash flows: $3000 at the end of 2 years,$2000 at the end of 4 years,and $1500 at the end of 6 years.Use a graphing calculator to graph the net present value as a function of the interest rate compounded annually.Determine the interest rate for which the investment is profitable.

Question 71

A debt of $12,000,which is due 10 years from now,is instead to be paid off by four payments: $3000 now,$2000 in 3 years,$2000 in 6 years,and a final payment at the end of 8 years.What would this payment be if an interest rate of 5.5% compounded semiannually is assumed?

Question 72

How much must be invested at an interest rate of 9.6% compounded monthly to have $3000 in five years?

Question 73

A trust fund for a 12-year-old child is being set up by a single payment so that when the child is 21 there will be $24,000.If the fund earns interest at the rate of 7.25% compounded quarterly,how much money should be paid into the fund initially?

Question 74

Miguel has the opportunity to invest $3000 in a friend's business such that he will be repaid $4500 in six years.If he instead wanted to put the $3000 into a savings account,what interest rate compounded monthly would be needed to equal the investment?

Question 75

Miguel has the opportunity to invest $3000 in a friend's business such that he will be repaid $4500 in six years.On the other hand,he can put the $3000 in a savings account that pays 5.5% compounded quarterly.Which investment is better?

Question 76

A trust fund for a child's education is being set up by a single payment so that at the end of 17 years there will be $31,000.If the fund earns interest at the rate of 8.25% compounded monthly,how much money should be paid into the fund initially?

Question 77

Suppose that you can invest $11,000 in a business that guarantees you the following cash flows: $5500 at the end of 2 years,$4500 at the end of 4 years,and $4000 at the end of 5 years.Assuming an interest rate of 6.25% compounded annually,find the net present value of the cash flows.Is the investment profitable?

Question 78

Suppose Mr.Takegawa owes Ms.Perez three sums of money: $1000 due in 2 years,$1500 due in 5 years,and $2000 due in 8 years.Suppose he would rather pay her $2000 now and the rest in 3 years.If the interest rate is 6% compounded annually,how much will he owe in 3 years?

Question 79

Suppose you have the opportunity to invest $6000 in a business venture such that you will be repaid $8000 in five years.On the other hand,you can put the $6000 in a savings account that pays 5.25% compounded monthly.Which investment is better?

Question 80

Suppose that Tori can invest $13,000 in a business that guarantees her the following cash flows: $6000 at the end of 2 years,$5000 at the end of 4 years,and $4000 at the end of 6 years.Assuming an interest rate of 6% compounded monthly,find the present value of the cash flows.Is the investment profitable?