Deck 3: The Mathematics of Finance

Question 1

Find the present value of the decreasing annuity necessary to fund a withdrawal of $100 per month for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

A)$18,147.28
B) $18,031.09
C) $18,003.70
D) $19,127.80
E) $18,218.40

Answer 1

$18,031.09

Question 2

Find the periodic withdrawal for an annuity of $240,000 at 6%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

A) $P M T = \$ 4,648.94$
B) $P M T = \$ 1,048.94$
C) $P M T = \$ 6,205.22$
D) $P M T = \$ 3,095.97$
E) $P M T = \$ 1,546.32$

Answer 2

$P M T = \$ 4,648.94$

Question 3

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 25 years at 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round answer to the nearest cent. ​

A)$169,050.86
B) $676,203.46
C) $1,690,508.64
D) $426,203.46
E) $104,000.00

Answer 3

$426,203.46

Question 4

Determine the selling price, per $1,000 maturity value, of a 10-year, 4.885% bond, with a yield of 4.890%. (Assume twice-yearly interest payments.) Round your answer to the nearest cent. ​

A)$999.61
B) $382.75
C) $1,002.60
D) $621.45
E) $616.86

Question 5

Find the periodic withdrawal for an annuity of $75,000 at 4%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

A) $P M T = \$ 1,188.43$
B) $P M T = \$ 439.93$
C) $P M T = \$ 145.88$
D) $P M T = \$ 1,189.93$
E) $P M T = \$ 395.88$

Question 6

Find the present value of a decreasing annuity necessary to fund withdrawals of $1,100 per month for 10 years, if the annuity earns 6% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

A)$94,738.99
B) $99,080.80
C) $97,153.15
D) $94,739.49
E) $95,628.67

Question 7

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

A)$244.24 per month
B) $220.71 per month
C) $281.72 per month
D) $286.72 per month
E) $186.89 per month

Question 8

Find the periodic withdrawal for an annuity containing $275,000 at 6%, paid out monthly for 30 years. (Assume end-of-period deposits and compounding at the same intervals as deposits). Round your answer to the nearest cent.

A) $P M T = \$ 1,476.26$
B) $P M T = \$ 1,829.58$
C) $P M T = \$ 1,647.84$
D) $P M T = \$ 1,650.26$
E) $P M T = \$ 1,648.76$

Question 9

Find the amount accumulated in the increasing annuity of $200 deposited monthly for 5 years at 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

A)$92,929.34
B) $24,720.00
C) $12,929.34
D) $4,646.47
E) $1,292.93

Question 10

Find the amount accumulated in an increasing annuity in which $100 is deposited monthly for 20 years at 5% per year in an account containing $10,000 at the start. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

A)$68,229.77
B) $41,103.37
C) $51,172.33
D) $40,937.86
E) $27,537.44

Question 11

Determine the periodic payment for a loan of $25,000 borrowed at 6% for 7 years, with monthly payments. Round your answer to the nearest cent. ​

A)$365.21
B) $241.68
C) $7.73
D) $307.86
E) $351.73

Question 12

Find the present value of a decreasing annuity necessary to fund withdrawals of $2,500 per quarter for 20 years, if the annuity earns 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits). Round your answer to the nearest cent.

A) $P V = \$ 137,220.52$
B) $P V = \$ 175,298.95$
C) $P V = \$ 75,500.91$
D) $P V = \$ 45,113.88$
E) $P V = \$ 75,501.91$

Question 13

Find the periodic withdrawal for an annuity of $140,000 at 5%, paid out monthly for 17 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

A) $P M T = \$ 436.78$
B) $P M T = \$ 408.45$
C) $P M T = \$ 1,018.13$
D) $P M T = \$ 1,020.12$
E) $P M T = \$ 522.04$

Question 14

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent. ​

A)$267.77 per month
B) $186.89 per month
C) $244.24 per month
D) $206.76 per month
E) $201.58 per month

Question 15

Find the amount accumulated in the increasing annuity of $150 deposited monthly for 15 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

A)$4,755.83
B) $40,093.34
C) $7,609.33
D) $76,093.34
E) $18,900.00

Question 16

Determine the quarterly payment necessary to accumulate $65,000 in a fund paying 8% per year, compounded quarterly, for 10 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent. ​

A)$1,034.01 per quarter
B) $1,038.64 per quarter
C) $1,099.65 per quarter
D) $1,133.47 per quarter
E) $1,076.12 per quarter

Question 17

While shopping for a car loan, you get the following offers: Solid Savings & Loan is willing to loan you $25,000 at 13% interest for 5 years. Fifth Federal Bank & Trust will loan you the $25,000 at 7% for 6 years. Both require monthly payments. You can afford $500 per month. Which loan, if either, can you take

A)Both
B) Fifth Federal Bank & Trust
C) Neither
D) Solid Savings & Loan

Question 18

Determine the periodic payment for a loan of $200,000 borrowed at 3% for 15 years, with monthly payments. Round your answer to the nearest cent. ​

A)$1,404.69
B) $1,438.51
C) $1,381.16
D) $1,368.68
E) $1,373.68

Question 19

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 10 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

A)$105,000.00
B) $328,723.89
C) $1,027,262.16
D) $328,643.89
E) $128,723.89

Question 20

Find the present value of the decreasing annuity necessary to fund a withdrawal of $1,500 per quarter for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

A)$90,125.41
B) $90,765.53
C) $89,965.31
D) $90,204.49
E) $89,991.66

Question 21

Find the present value of a decreasing annuity necessary to fund withdrawals of $800 per month for 10 years, if the annuity earns 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________

Question 22

Find the amount accumulated in the increasing annuity of $100 deposited monthly for 10 years at 8% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________

Question 23

Find the amount accumulated in the increasing annuity in which $2,000 is deposited quarterly for 10 years at 7% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________

Question 24

Find the monthly payment necessary to accumulate $10,000 in an increasing annuity paying 2% per year, with monthly payments for 7 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________ per month

Question 25

Determine the periodic payment for a loan of $300,000 borrowed at 3% for 30 years, with quarterly payments. Round your answer to the nearest cent.
​
$__________

Question 26

Find the periodic withdrawal for an annuity of $50,000 at 5%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________

Question 27

Determine the periodic payment for a loan of $25,000 borrowed at 8% for 5 years, with monthly payments. Round your answer to the nearest cent.
​
$__________

Question 28

While shopping for a car loan, you get the following offers: Solid Savings & Loan is willing to loan you $30,000 at 14% interest for 6 years. Fifth Federal Bank & Trust will loan you the $30,000 at 10% for 4 years. Both require monthly payments. You can afford $690 per month. Which loan, if either, can you take

Question 29

Find the amount accumulated in an increasing annuity in which $200 is deposited monthly for 20 years at 3% per year in an account containing $10,000 at the start. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​ $ __________.

Question 30

Find the present value of a decreasing annuity necessary to fund withdrawals of $2,000 per quarter for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits). Round your answer to the nearest cent.
​
$__________

Question 31

Find the amount accumulated in the increasing annuity in which $150 is deposited monthly for 20 years at 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________

Question 32

Determine the quarterly payment necessary to accumulate $100,000 in a fund paying 7% per year, compounded quarterly, for 19 years. Assume end-of-period deposits and compounding at the same intervals as deposits. (Round your answer to the nearest cent.)
​
$__________ per quarter

Question 33

Find the periodic withdrawal for an annuity of $100,000 at 3%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________

Question 34

Find the periodic withdrawal for an annuity of $200,000 at 4%, paid out monthly for 11 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________

Question 35

Find the present value of the decreasing annuity necessary to fund a withdrawal of $1,300 per quarter for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​ $ __________.

Question 36

Find the amount accumulated in the increasing annuity of $1,600 deposited quarterly for 10 years at 6% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________

Question 37

Find the present value of the decreasing annuity necessary to fund a withdrawal of $200 per month for 20 years, if the annuity earns 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​ $ __________.

Question 38

Determine the monthly payment necessary to accumulate $40,000 in a fund paying 8% per year, compounded monthly, for 6 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
​
$__________ per month

Question 39

Determine the selling price, per $1,000 maturity value, of a 10-year, 4.835% bond, with a yield of 4.87%. (Assume twice-yearly interest payments.) Round your answer to the nearest cent.
​
$__________

Question 40

Find the periodic withdrawal for an annuity containing $225,000 at 3%, paid out monthly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits). Round your answer to the nearest cent.
​
$__________

Question 41

Calculate the future value of an investment of $14,000 at 5.5% per year, compounded weekly, after 6 years. Assume 52 weeks per year. ​

A)$19,827.28
B) $20,141.40
C) $19,470.16
D) $19,342.01
E) None of these

Question 42

Calculate, to the nearest 0.1%, what annual interest rate would be required if you invested $6,000 in Apple stock and ended up with $15,622 when you sold the stock after 5 years Assume that interest was compounded quarterly. ?

A)19.4%
B) 19.6%
C) 20.0%
D) 20.2%
E) None of these

Question 43

Calculate, to the nearest cent, the present value of an investment that will be worth $16,000 after 7 years, at 7.4% compounded quarterly.

A) $P V = \$ 9,546.55$
B) $P V = \$ 15,326.06$
C) $P V = \$ 9,707.11$
D) $P V = \$ 15,337.91$
E) $P V = \$ 9,576.59$

Question 44

Calculate the future value of an investment of $3,500, after one year, if it is deposited in a savings account that is compounded quarterly at an annual rate of 11%. Round your answer to the nearest cent. ​

A)$3,900.00
B) $4,100.95
C) $4,235.00
D) $3,901.17
E) None of these

Question 45

You are offered three investments. What is the best investment ?

A)The first promises to earn 20% compounded annually.
B) The second will earn 19.5% compounded quarterly.
C) The third will earn 19% compounded weekly.

Question 46

Calculate, to the nearest cent, the present value of an investment that will be worth $4,000 after 9 years, at 10% per year, compounded annually.

A) $P V = \$ 3,712.13$
B) $P V = \$ 1,696.39$
C) $P V = \$ 3,619.52$
D) $P V = \$ 4,444.44$
E) $P V = \$ 1,632.35$

Question 47

Inflation has been running 6% per year. A car now costs $32,000. How much would it have cost 9 years ago

A)$18,940.00
B) $18,335.83
C) $19,090.75
D) $18,940.75
E) None of these

Question 48

How much would you have to invest when you are 20 years old at 9% compounded monthly to end up with a million dollars by age 48 Round your answer to the nearest thousand. ?

A)$171,000
B) $81,000
C) $166,000
D) $89,000
E) None of these

Question 49

Find the effective annual interest rate of 17% compounded monthly. ​

A)18.50%
B) 18.39%
C) 18.11%
D) 18.53%
E) 17.72%

Question 50

Calculate the future value of an investment of $5,000 at 0.8% per year, compounded monthly, after 8 years. Round your answer to the nearest cent. ​

A)$5,330.35
B) $5,202.20
C) $5,329.10
D) $5,687.47
E) $4,659.11

Question 51

Determine the amount of money, to the nearest dollar, you must invest now at 5% per year compounded annually, so that you will be a millionaire in 50 years.

A)$78,440
B) $82,512
C) $81,803
D) $87,204
E) $83,677

Question 52

$10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 6%. Find the total amount accumulated at the end of 5 years. Round your answer to the nearest cent. ​

A)$13,289.59
B) $33,000.00
C) $13,488.50
D) $11,489.08
E) None of these

Question 53

Calculate the present value of an investment that will be worth $2,000 after 3 years at 8% per year compounded annually. Round your answer to the nearest cent. ​

A)$1,587.66
B) $1,574.51
C) $1,715.81
D) $2,258.90
E) $1,944.78

Question 54

You invest $13,000 in Rapid Growth Funds, which appreciate by 2% per year, with yields reinvested quarterly. By how much will your investment have grown after 7 years Round your answer to the nearest cent. ?

A)$461.88
B) $9,633.31
C) $1,932.91
D) $1,948.34
E) None of these

Question 55

Find the effective annual interest rate of 4% compounded quarterly. ​

A)4.31%
B) 4.25%
C) 4.75%
D) 4.06%
E) None of these

Question 56

The effective rate exceeds the nominal rate when the interest is compounded more than once a year resulting in a larger effective rate.

Question 57

Calculate, to the nearest cent, the future value of an investment of $28,000 at 10.45% per year, compounded monthly, after 14 years.

A) $F V = \$ 120,165.64$
B) $F V = \$ 112,584.37$
C) $F V = \$ 821,798.19$
D) $F V = \$ 31,613.79$
E) $F V = \$ 45,502.17$

Question 58

Find the effective annual interest rate of 11% compounded monthly. Round your answer to the nearest 0.01%.

A) $r _ { \text {eff } } = 11.62 \%$
B) $r _ { \text {eff } } = 132.00 \%$
C) $r _ { \text {eff } } = 1.12 \%$
D) $r _ { \text {eff } } = 11.57 \%$
E) $r _ { \text {eff } } = 11.47 \%$

Question 59

Calculate, to the nearest cent, the future value of an investment of $14,000 at 4.25% per year, compounded quarterly (4 times per year), after 7 years.

A) $F V = \$ 18,821.28$
B) $F V = \$ 14,607.35$
C) $F V = \$ 44,901.19$
D) $F V = \$ 18,735.29$
E) $F V = \$ 15,075.03$

Question 60

Doubling the frequency of compounding in a compound interest investment will not double the amount of the interest.

Question 61

Find the effective annual interest rate of 13% compounded monthly. Round your answer to the nearest 0.01%.
​ __________ %

Question 62

You deposit $1,500 in an account at the Lifelong Trust Savings and Loan that pays 6% per year compounded quarterly. By how much will your deposit have grown after 8 years Round the answer to the nearest cent. ?

A)$3,165.49
B) $915.39
C) $915.49
D) $2,415.49
E) $912.39

Question 63

Calculate, to the nearest cent, the future value of an investment of $22,000 at 6% per year, compounded monthly, after 12 years.
​
​FV​ = $__________

Question 64

During a prolonged recession, property values on Long Island depreciated by 8% every six months. If my house cost $200,000 originally, how much was it worth 5 years later Round your answer to the nearest cent. ?

A)$86,877.39
B) $86,877.69
C) $86,878.79
D) $86,878.69
E) $86,882.69

Question 65

Calculate, to the nearest cent, the future value of an investment of $12,000 at 4.5% per year, compounded quarterly, after 5 years.
​
FV = $__________

Question 66

Calculate, to the nearest cent, the future value of an investment of $12,000 at 7% per year, compounded annually, after 11 years.
​
​FV​ = $__________

Question 67

If Brazil has an annual inflation rate of 11% and an item will cost 125,000 reals in 3 years, what does the same item cost now Round to the nearest real. ?

A)91,389 reals
B) 91,399 reals
C) 91,394 reals
D) 172,355 reals
E) 173,610 reals

Question 68

The nominal rate exceeds the effective rate when the interest is compounded _________ once a year resulting in a larger effective rate. ​

A)less or equally than
B) equally
C) more or equally than
D) less than
E) more than

Question 69

Inflation is running at 2.4% per year when you deposit $11,000 in an account earning 6.5% per year compounded quarterly. In constant dollars, how much money will you have 4 years from now Round your answer to the nearest cent. [Hint: First calculate the value of your account in 4 year's time, and then find its present value based on the inflation rate.]

A)$12,965.96
B) $12,921.51
C) $12,947.97
D) $12,937.97
E) $12,870.38

Question 70

When I was considering what to do with my $7,500 Lottery winnings, my broker suggested I invest half of it in gold, whose value was growing by 11% per year, and the other half in certificates of deposit (CDs), which were yielding 9% per year compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 7 years Round your answer to the nearest cent.

$ __________

Question 71

Find the effective annual interest rate of 7% compounded daily. Assume 365 days per year. Round your answer to the nearest 0.01%.

A) $r _ { \text {eff } } = 7.25 \%$
B) $r _ { \text {eff } } = 25.55 \%$
C) $r _ { \text {eff } } = 7.30 \%$
D) $r _ { \text {eff } } = 7.35 \%$
E) $r _ { \text {eff } } = 1.92 \%$

Question 72

My recent marketing idea, the Miracle Algae Growing Kit, has been remarkably successful, with monthly sales growing by 5% every 6 months over the past 3 years. Assuming that I sold 450 kits the first month, what is the present rate of sales Round your answer to the nearest whole number. ?

A)603 kits per month
B) 524 kits per month
C) 485 kits per month
D) 486 kits per month
E) 522 kits per month

Question 73

Calculate, to the nearest cent, the present value of an investment that will be worth $2,000 after 17 years, at 4% per year, compounded annually.
​
​PV​ = $__________

Question 74

When I was considering what to do with my $8,000 Lottery winnings, my broker suggested I invest half of it in gold, whose value was growing by 12% per year, and the other half in certificates of deposit (CDs), which were yielding 9% per year compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 7 years Round your answer to the nearest cent. ?

A)$16,609.89
B) $16,250.51
C) $16,154.88
D) $13,422.30
E) $16,719.70

Question 75

Find the effective annual interest rate of 4% compounded monthly. Round your answer to the nearest 0.01%.
​
r_eff = __________ %

Question 76

Calculate, to the nearest cent, the present value of an investment that will be worth $14,000 after 5 years, at 7% compounded monthly.
​
PV​ = $__________

Question 77

Doubling the frequency of compounding in a compound interest investment ________ double the amount of the interest. ​

A)will
B) will not

Question 78

Find the effective annual interest rate of 10% compounded daily. Assume 365 days per year. Round your answer to the nearest 0.01%.
​ __________ %

Question 79

When I was considering what to do with the $6,000 proceeds from my sale of technology stock, my broker suggested I invest half of it in municipal bonds, whose value was growing by 15% per year, and the other half in certificates of deposit (CDs), which were yielding 7% per year compounded every 2 months. Assuming that these rates are sustained, how much will my investment be worth in 8 years Round your answer to the nearest cent. ?

A)$14,412.19
B) $9,177.07
C) $14,412.09
D) $5,235.02
E) $14,411.09

Question 80

When I was considering what to do with the $9,000 proceeds from my sale of technology stock, my broker suggested I invest half of it in municipal bonds, whose value was growing by 12% per year, and the other half in certificates of deposit (CDs), which were yielding 3% per year compounded every 2 months. Assuming that these rates are sustained, how much will my investment be worth in 12 years Round your answer to the nearest cent.

$ __________