Math 1030-5
Test 2
You will have 50 minutes to complete this test. You may use a calculator on this test. I have provided a list of
formulas on the last page of the test. Please remember that you must show your work in order to receive credit.
For example, if you can do an entire problem by punching it into your calculator, you must still tell me what you
punched in. Good luck!
1. In a recent year, Saudi Arabia produced 8.2 million barrels of crude oil per day, while the United States
produced 6.4 million barrels per day. What is the absolute difference? What is the relative difference? (Use the
U.S. value for the reference value.)
absolute difference = 8.2 million barrels − 6.4 million barrels = 1.8 million barrels
relative difference =
1.8 million barrels
= .281 = 28.1%
6.4 million barrels
2. You receive a pay raise of 5% and then receive a pay cut of 5%. If your original salary was S, what is your
new salary?
after pay raise: S + .05S = 1.05S.
after pay cut: 1.05S − .05 × 1.05S = (1.05 − .053)S = .997S
After the pay raise and the pay cut, you make 99.7% of what you did originally.
3. In one of the homework exercises, we found that the sun radiates 3.171 × 1026 Js , and the U.S. annual energy
J
., so the sun produces more than enough energy in one second to satisfy the energy
consumption is only 1 × 1020 yr
needs of the U.S. for a year. If we could really capture all the energy radiated from the sun in 1 second, for how
many years would the U.S. be supplied with energy?
3.171 × 1026 J
= 3, 171, 000 years.
J
1 × 1020 yr
4. If 1 foot on a map represents 100 meters in reality, what is the scale ratio for this map?
1 ft ×
1m
12 in 2.54 cm
×
×
= .305 m.
1 ft
1 in
100 cm
.305 m
= .00305.
100 m
5. Multiply the masses 9.7 kilograms and 165 kilograms to the correct number of significant digits.
We have that 9.7 × 165 = 1600.50. The correct number of significant digits is two, since 9.7 has two significant
digits and 165 has three. In multiplication, we always round to the same number of significant digits as the
number in the problem with the fewest significant digits has. Thus, the correct answer is 1600 kg 2 .
6. You invest $1,000 in an account that pays simple interest of 5% for 5 years. How much will you have at the
end of the five years?
Each year you earn 1000 × .05 = 50 dollars in interest. Over 5 years, you earn $50 × 5 = $250 in interest. Adding
in the principal, you have $1250 total.
7. You make a $1000 deposit in an account that has an APR of 5% with quarterly compounding. How much is
in the account after 5 years?
nY
4×5
.05
AP R
= 1000 1 +
= $1282.04.
A=P 1+
n
4
1
8. What is the annual percentage yield for an account with an APR of 5% and continuous compounding?
AP Y =
P e.05(1) − P
= e.05 − 1 = .051.
P
9. You put $200 per month in an investment plan that pays an APR of 7%. How much money will you have after
18 years? What is the total amount of deposits made in this period?
h
h
i
i
nY
12×18
1 + APn R
1 + .07
−1
−1
12
= $86, 144.21
A = PMT ×
= 200 ×
.07
AP R
12
n
deposits = 200 × 12 × 18 = $43, 200.
10. You pay $8,000 for a municipal bond. When it matures after 20 years, you receive $12,500. What are the
total and annual returns for this investment?
12, 500 − 8, 000
A−P
=
= .563 = 56.3%
P
8, 000
Y1
1
A
12, 500 20
annual return =
−1=
− 1 = .023 = 2.3%
P
8, 000
total return =
11. Suppose you have a home mortgage of $150,000 with a fixed APR of 7.5% for 15 years.
(a) Calculate the monthly payment.
(b) Determine the total payment over the term of the loan.
(c) Determine how much of the total payment over the loan term goes to principal and how much to interest.
P×
(a) P M T = h
1− 1+
AP R
n
AP R −nY
n
150, 000 × .075
12
i= h
−12×15 i = $1, 390.52.
1 − 1 + .075
12
(b) total payment = 1, 390.52 × 12 × 15 = $250, 293.60
(c) interest = 250, 293.60 − 150, 000 = $100, 293.60,
principal = $150, 000
12. The number of cells in a tumor doubles every 1.5 months. If the tumor begins as a single cell, how many cells
will there be after 4 years?
t
48
new value = initial value × 2 Tdouble = 1 × 2 1.5 = 4, 294, 967, 296.
13. The current population of a threatened animal species is 1 million, but it is declining with a half-life of 10
years. How many animals will be left in 70 years?
T t
70
1 half
1 10
6
new value = initial value ×
= 1 × 10 ×
= 7, 812.5
2
2
14. Spending by consumers is growing at a rate of 12% per year. Find the doubling time using
(a) the approximate formula
(b) the exact formula
70
70
=
= 5.833
P
12
log10 (2)
log10 (2)
=
= 6.116
=
log10 (1 + r)
log10 (1 + .12)
(a) Tdouble ≈
(b) Tdouble
2
Formulas and Other Useful Information
AD = CV − RV
T2 = −
log10 2
log10 (1 + r)
RD =
AD
RV
A = P × (1 + i)N
1 in = 2.54 cm
(nY )
AP R
A=P 1+
n
Tt
1 2
N V = IV ×
2
A = P × e(AP R×Y )
Y1
A
AR =
−1
P
T1 ≈
70
P
A = P × (1 + AP R)Y
70
P
A1 − P
AP Y =
P
i
h
AP R (nY )
−1
1+ n
A = PMT ×
AP R
T2 ≈
n
(A − P )
TR =
P
p
gr = r × 1 −
cc
log10 2
T1 =
log10 (1 + r)
P × APn R
PMT = h
(−nY ) i
1 − 1 + APn R
t
N V = IV × 2 T1
3