Deck 3: Additional Derivative Topics

Question 1

Use the formula A = P(1 + rt) to find the indicated quantity.
P = $7996; r = 6%; t = 10 months. Find A.

A) $8475.76
B) $8395.80
C) $399.80
D) $6663.33

Answer 1

$8395.80

Question 2

Use I = Prt for simple interest to find the indicated quantity.
P = $3000; t = 90 days; I = $105. Find r. (Use 360 days in a year.)

A) 3.5%
B) 14.2%
C) 9.7%
D) 14.0%

Answer 2

14.0%

Question 3

Find the amount that will be accumulated in the account under the given conditions.
The principal $15,400 is accumulated with simple interest of 16% for 5 years.

A) $20,212.50
B) $27,720
C) $12,320
D) $15,892.80

Answer 3

$27,720

Question 4

Solve the problem. Assume that simple interest is being calculated in each case. Round your answer to the nearest cent.
John Lee's savings account has a balance of $4466. After 15 months, what will the amount of interest be at 2.8% per year?

A) $140.05
B) $125.05
C) $156.31
D) $297.73

Question 5

Use I = Prt for simple interest to find the indicated quantity.
P = $22,660; r = 13%; 2.4 years. Find I.

A) $15,590.08
B) $7069.92
C) $29,729.92
D) $2945.80

Question 6

Use I = Prt for simple interest to find the indicated quantity.
I = $750; r = 6%; t = 6 months. Find P.

A) $22.50
B) $25,750
C) $24,250
D) $25,000

Question 7

Convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal
form.
11.6% to decimal

A) 11.6
B) 116
C) 0.116
D) 0.00116

Question 8

Provide an appropriate response.
If you pay $5,500 for a simple interest note that will be worth $6,000 in 21 months, what annual simple interest
rate will you earn? (Compute the answer to one decimal place.)

Question 9

Make the indicated conversion. Assume a 360-day year as needed.
8 months to simplified fraction of a year

A)
B)
C)
D)

Question 10

Solve the problem. Round dollar amounts to the nearest cent. Use 360 days.
HarbourTown Marina purchased four boat lifts for raising and lowering large boats into the water. The boat lifts cost $61,300 each. They borrowed the money from the bank for 240 days at 10%. Find the maturity value.

A) $65,386.67
B) $261,546.67
C) $67,430.00
D) $269,720.00

Question 11

Solve the problem. Round dollar amounts to the nearest cent. Use 360 days.
Polson Associates bought a new computer system. To pay for the system, they borrowed $41,950 from the bank at t interest for 130 days. Find the simple interest.

A) $3670.63
B) $1315.31
C) $1325.50
D) $1307.35

Question 12

Make the indicated conversion. Assume a 360-day year as needed.
150 days to a simplified fraction of year

A)
B)
C)
D)

Question 13

Provide an appropriate response.
Find the amount due on a loan of $8,500 at 7.5% simple interest at the end of 4 years.

Question 14

Use I = Prt for simple interest to find the indicated quantity.
P = $13,500; t = 4 months; I = $517.50. Find r.

A) 7.7%
B) 11.5%
C) 11.7%
D) 3.8%

Question 15

Convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal
form.
0.05% to decimal

A) 0.5
B) 5.0
C) 0.0005
D) 0.05

Question 16

Use the formula A = P(1 + rt) to find the indicated quantity.
A = $16,400; r = 10%; 90 days. Find P.

A) $16,400
B) $400.00
C) $16,000
D) $16,810

Question 17

Convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal
form.
0.25 to percent

A) 0.0025%
B) 25%
C) 2.5%
D) 2.25%

Question 18

Convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal
form.
0.05 to percent

A) 0.0005%
B) 50%
C) 0.05%
D) 5%

Question 19

Use the formula A = P(1 + rt) to find the indicated quantity.
Allan borrowed $5500 from his father to buy a car. He repaid him after 10 months with interest of 5% per year. Find the total amount he repaid.

A) $229.17
B) $5775.00
C) $5706.25
D) $5729.17

Question 20

Solve the problem. Round dollar amounts to the nearest cent. Use 360 days.
What is the purchase price of a 26-week T-bill with a maturity value of $1000 that earns an annual interest rate of 5.25%?

A) $1000
B) $25.58
C) $974.42
D) $1025.58

Question 21

Provide an appropriate response.
An investment company pays 7% compounded quarterly. What is the effective rate? (Compute the answer to
two decimal places).

Question 22

Provide an appropriate response.
If an investor buys a 39-week T-bill with a maturity value of $25,000 for $23,543 what annual interest rate
(annual yield) will the investor earn? (Express your answer as a percentage, correct to one decimal place.)

Question 23

Provide an appropriate response.
How much should you invest now at 6% compounded semiannually to have $8,500 to buy a car in 2.5 years?

Question 24

Find the compound interest earned. Round to the nearest cent.
$14,000 at 5% compounded annually for 3 years

A) $2100.00
B) $1435.00
C) $701.50
D) $2206.75

Question 25

Find the compound amount for the deposit. Round to the nearest cent.
$15,000 at 10% compounded semiannually for 10 years

A) $39,799.47
B) $24,433.42
C) $38,906.14
D) $30.000.00

Question 26

Use the average daily balance method to compute the amount of interest that will be charged at the end of the billing
cycle. Use a 365-day year.
Month: February (28 days) Previous month's balance: $1240
Interest rate: 22%

A) $15.96
B) $19.71
C) $18.22
D) $8.31

Question 27

Find the compound amount for the deposit. Round to the nearest cent.
$600 at 8% compounded quarterly for 5 years

A) $840.00
B) $881.60
C) $662.45
D) $891.57

Question 28

Solve the problem. Assume that the minimum payment on a credit card is the greater of $27 or 3% of the unpaid balance.
Find the minimum payment on an unpaid balance of $1584.40.

A) $52.53
B) $47.53
C) $27.00
D) $475.32

Question 29

Solve the problem. Assume that the minimum payment on a credit card is the greater of $27 or 3% of the unpaid balance.
Find the minimum payment on an unpaid balance of $787.71.

A) $28.63
B) $236.31
C) $23.63
D) $27.00

Question 30

Find the compound interest earned. Round to the nearest cent.
$600 at 5% compounded quarterly for or

A) $204.06
B) $95.82
C) $95.45
D) $46.43

Question 31

Provide an appropriate response.
An investor purchased 150 shares of a stock at $15.80 per share. The investor holds the stock for 39 weeks and then sells
the stock for $19.25 per share. Use the commission schedule for this company given below to find the annual rate of
interest earned by this investor. Express your answer as a percentage, correct to one decimal place.

Question 32

Use the average daily balance method to compute the amount of interest that will be charged at the end of the billing
cycle. Use a 365-day year.
Month: April (30 days) Previous month's balance: $960
Interest rate: 21%

A) $14.93
B) $14.07
C) $11.61
D) $17.50

Question 33

Provide an appropriate response.
What amount will be in an account after 1.5 years if $4,000 is invested at 5% compounded semiannually?

Question 34

Use the average daily balance method to compute the amount of interest that will be charged at the end of the billing
cycle. Use a 365-day year.
Month: May (31 days) Previous month's balance: $960
Interest rate: 19%

A) $7.88
B) $12.35
C) $11.31
D) $8.76

Question 35

Solve the problem.
How long will it take for $3000 to grow to $22,600 at an interest rate of 3.1% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

A) 6.51 yr
B) 65.14 yr
C) 0.65 yr
D) 6513.99 yr

Question 36

Find the compound interest earned. Round to the nearest cent.
$700 at 8% compounded semiannually for 4 years

A) $252.34
B) $595.65
C) $258.00
D) $118.90

Question 37

Use the average daily balance method to compute the amount of interest that will be charged at the end of the billing
cycle. Use a 365-day year.
Month: July (31 days) Previous month's balance: $840
Interest rate: 20%

A) $10.56
B) $12.40
C) $10.66
D) $10.92

Question 38

Solve the problem. Assume that the minimum payment on a credit card is the greater of $27 or 3% of the unpaid balance.
If the annual interest rate is 15.99%, find the difference between the minimum payment and the interest owed on an unpaid balance of $748.44 that is 1 month overdue.

A) $12.54
B) $13.10
C) $17.03
D) $14.03

Question 39

Provide an appropriate response.
An investor purchased 500 shares of a stock at $19 per share. The commission she paid to buy the stock was $65
plus 0.3% of the principal amount. Six months later she sold the stock for $20.50 per share. If she paid the same
rate of commission to sell the stock, what annual rate of interest (annual yield) did she earn on her initial
investment (including purchase price plus commission)? Express your answer as a percentage, correct to one
decimal place.

Question 40

Find the compound amount for the deposit. Round to the nearest cent.
$1100 at 3% compounded quarterly for 2 years

A) $1116.56
B) $1167.76
C) $1166.99
D) $1166.00

Question 41

Solve the problem. Round to the nearest cent as needed.
Samantha's savings account has a balance of $4643. After 25 years, what will the amount of interest be at 6% compounded annually?

A) $15,289.16
B) $15,275.16
C) $15,284.16
D) $2785.80

Question 42

What is the annual percentage yield (APY) for money invested at the given annual rate? Round results to the nearest
hundredth of a percent.
3.5% compounded continuously.

A) 3.50%
B) 3.53%
C) 3.55%
D) 3.56%

Question 43

What is the annual percentage yield (APY) for money invested at the given annual rate? Round results to the nearest
hundredth of a percent.
5% compounded semiannually

A) 5.06%
B) 5.13%
C) 5.00%
D) 5.09%

Question 44

Find i (the rate per period) and n (the number of periods) for the annuity.
Semiannual deposits of $400 are made for 10 years into an annuity that pays 7% compounded semiannually.

A) i = 0.07; n = 10
B) i = 0.035; n = 20
C) i = 0.35; n = 10
D) i = 0.0175; n = 40

Question 45

Find i (the rate per period) and n (the number of periods) for the annuity.
Monthly deposits of $1600 are made for 6 years into an annuity that pays 9% compounded monthly.

A) i = 0.75; n = 12
B) i = 0.0075; n = 72
C) i = 0.75; n = 6
D) i = 0.09; n = 72

Question 46

Use the future value formula to find the indicated value. Round to three decimal places.
n = 10; i = 0.02; PMT = $1; FV = ?

A) $10.95
B) $60.95
C) $12.169
D) $9.755

Question 47

Solve the problem. Round to the nearest cent as needed.
A child receives a $10,000 gift toward a college education from her grandparents on her first birthday. How
much money will it be worth in 17 years if it is invested at 8.25% compounded quarterly? Round your answer
to the nearest cent.

Question 48

Solve the problem. Round to the nearest cent as needed.
The bacteria in a 11-liter container double every 2 minutes. After 53 minutes the container is full. How long did it take to fill a quarter of the container?

A) 13.3 min
B) 26.5 min
C) 49 min
D) 39.8 min

Question 49

Solve the problem. Round to the nearest cent as needed.
Cheraw Auto Repair believes that it will need new equipment in 10 years. The equipment will cost $26,000. What lump sum should be invested today at 8% compounded semiannually, to yield $26,000?

A) $21,097.18
B) $17,462.98
C) $11,866.06
D) $17,637.61

Question 50

Solve the problem. Round to the nearest cent as needed.
How many months will it take until an account will have $3,500 if $2,500 is invested now at 5% compounded
monthly?

Question 51

Solve the problem.
The State Employees' Credit Union offers a 1-year certificate of deposit with an APY (or effective rate) of 5.5%. If interest is compounded quarterly, find the actual interest rate. Round to the nearest tenth of a percent.

A) 5.4%
B) 6.4%
C) 5.1%
D) 5.6%

Question 52

Solve the problem. Round to the nearest cent as needed.
A bank has $750,000 to lend for 7 months. It can lend it to a local contractor at a simple interest rate of 12%, or it can lend it to a small business that will pay 12% compounded monthly. If the bank wants to maximize its
Interest earned, who should receive the loan (contractor or business) and what is the additional interest earned?

A) Contractor; $52,500
B) Business; $1601.51
C) Contractor; $1601.51
D) Business; $54,101.51

Question 53

Solve the problem. Round to the nearest cent as needed.
Brandon's savings account has a balance of $4069. After 4 years what will the amount of interest be at 5% compounded quarterly?

A) $899.73
B) $894.73
C) $101.73
D) $885.73

Question 54

Solve the problem. Round to the nearest cent as needed.
The rabbit population in a forest area grows at the rate of 6% monthly. If there are 230 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. Use e

A) 447
B) 457
C) 483
D) 470

Question 55

Provide an appropriate response.
A bank account starts with $1,000 in it. Interest is paid at 6% annual interest, compounded monthly. Graph the
exact function for the amount in the account over the first 12 months. Use vertical scale [900, 1,200].

Question 56

Solve the problem. Round to the nearest cent as needed.
Cara knows that she will need to buy a new car in 3 years. The car will cost $15,000 by then. How much should she invest now at 12%, compounded quarterly, so that she will have enough to buy a new car?

A) $10,520.70
B) $12.594.29
C) $11,957.91
D) $9532.77

Question 57

Solve the problem. Round to the nearest cent as needed.
An actuary for a pension fund need to have $14.6 million grow to $22 million in 6 years. What interest rate compounded annually does he need for this investment to growth as specified. Round your answer to the
Nearest hundredth of a percent.

A) 0.07%
B) 7%
C) 7.7%
D) 7.07%

Question 58

What is the annual percentage yield (APY) for money invested at the given annual rate? Round results to the nearest
hundredth of a percent.
6% compounded quarterly

A) 6.14%
B) 6.09%
C) 6.18%
D) 6.00%

Question 59

Solve the problem. Round to the nearest cent as needed.
How long will it take for $8400 to grow to $14,600 at an interest rate of 9.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

A) 0.59 year
B) 0.06 year
C) 5.88 years
D) 58.81 years

Question 60

Solve the problem.
Jennifer invested $6000 in her savings account for 7 years. When she withdrew it, she had $9004.82. Interest was compounded continuously. What was the interest rate on the account? Round to the nearest tenth of a
Percent.

A) 5.7%
B) 5.95%
C) 5.9%
D) 5.8%

Question 61

Solve the problem. Round to the nearest cent.
Joe wants to start an SEP-IRA that will have $460,000 in it when he retires in 15 years. How much should he invest semiannually in his IRA to do this if the interest is 15% compounded semiannually?

A) $44.35.77
B) $17,612.13
C) $4790.74
D) $4448.77

Question 62

Find i (the rate per period) and n (the number of periods) for the loan at the given annual rate.
Annual payments of $378.80 are made for 8 years to repay a loan at 6.4% compounded annually.

A) i = 0.064; n = 8
B) i = 0.00533; n = 12
C) i = 0.064; n = 16
D) i = 0.008; n = 8

Question 63

Find the rate of interest required to achieve the conditions set forth.
If Jay bought a lot for $8,000 and sold it 15 years later for $24,000, what was her percentage rate of return on this investment if it was compounded annually?

A) 8.7104%
B) 9.6825%
C) 7.5990%
D) 3.7995%

Question 64

Solve for the missing value. Round to four decimal places.
n = 24; i = 0.09; PMT = $1; PV = ?

A) $12.5156
B) $9.5802
C) $9.7066
D) $9.8226

Question 65

Solve the problem.
You can afford monthly deposits of $200 into an account that pays 8% compounded monthly. How many
months will it be until you have $15,000 to buy a car? (Round up to the next higher month if not an integer.)

Question 66

Solve for the missing value. Round to four decimal places.
n = 30; i = 0.03; PMT = $100; PV = ?

A) $1960.0441
B) $4706.6287
C) $1918.1585
D) $2000.0441

Question 67

Find the rate of interest required to achieve the conditions set forth.
A = $32,000 P = $8,000
T = 20 years
Compounded quarterly

A) 3.4959%
B) 3.5489%
C) 6.9919%
D) 5.5310%

Question 68

Solve the problem.
A couple decides on the following savings plan for their child's college education. When the child is 6 months
old, and every 6 months thereafter, they will deposit $310 into a savings account paying 9.5% interest
compounded semi-annually. After the child's tenth birthday, having made 20 such payments, they will stop
making deposits and let the accumulated money earn interest, at the same rate, for 8 more years, until the child
is 18 years old and ready for college. How much money (to the nearest dollar) will be in the account when the
child is ready for college?

Question 69

Solve the problem.
If $300,000 is to be saved over 25 years, how much should be deposited monthly if the investment earns 8% interest compounded monthly?

A) $315.45
B) $180.48
C) $260.87
D) $216.62

Question 70

Solve the problem.
What is the future value of an ordinary annuity at the end of 3 years if $200 is deposited each quarter into an
account earning 6% compounded quarterly?

Question 71

Solve the problem. Round to the nearest cent.
Cara needs $9,000 in 12 years. What amount can she deposit at the end of each quarter at 6% interest compounded quarterly so she will have her $9,000?

A) $125.68
B) $133.23
C) $533.49
D) $129.37

Question 72

Find the periodic payment that will render the sum.
FV = $24,000, interest is 8% compounded monthly, payments made at the end of each month for 3 years

A) $1264.68
B) $7104.88
C) $592.07
D) $1927.72

Question 73

Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.
PMT = $7,500, i = 3% interest compounded semiannually for 3 years

A) $46,721.63
B) $38,642.00
C) $546,721.63
D) $265,225.00

Question 74

Solve the problem.
At the end of every 3 months, Judy deposits $100 into an account that pays 6% compounded quarterly. After 4 years, she puts the accumulated amount into a certificate of deposit paying 7.5% compounded semiannually for
1 year. When this certificate matures, how much will Judy have accumulated?

A) $1930.25
B) $1823.20
C) $1920.96
D) $2072.31

Question 75

Use the future value formula to find the indicated value. Round to three decimal places.
n = 13; i = 0.04; PMT = $1000; FV = ?

A) $16,627.838
B) $18,292.371
C) $15,026.247
D) $41,627.144

Question 76

Find i (the rate per period) and n (the number of periods) for the loan at the given annual rate.
Quarterly Payments of $3000 are made for 4 years to repay a loan at 10.2% compounded quarterly.

A) i = 0.102; n = 16
B) i = 0.0255; n = 16
C) i = 0.0255; n = 4
D) i = 0.006375; n = 4

Question 77

Find the rate of interest required to achieve the conditions set forth.
A = $32,000 P = $8,000
T = 20 years
Compounded annually

A) 7.1773%
B) 8%
C) 3.5265%
D) 5.6467%

Question 78

Solve the problem. Round to the nearest cent.
Larry wants to start an IRA that will have $620,000 in it when he retires in 26 years. How much should he invest semiannually in his IRA to do this if the interest is 6% compounded semiannually?

A) $5094.65
B) $3969.83
C) $16,081.74
D) $5081.65

Question 79

Solve the problem.
You deposit $130 each month into a savings account that pays 5.5% compounded monthly. How much interest
will you have earned after 8 years?

Question 80

Solve the problem.
An ordinary annuity has a value of $1,333.85 at the end of 4 years when $150 is deposited every 6 months into
an account earning 6% compounded semiannually. How much interest has been earned?