Math 1030-7 Midterm 2
Name:
Instructions: There are TWO parts in this exam, FIVE problems in each
part. Answer the questions in the spaces provided on the question sheets.
If you need more space, use the bottom of the last page, but remember to
indicate which problem you are doing. Partial credit will be awarded. Scientific
calculators are allowed. This exam is closed book and closed notes. Show you
work on each problem.
The formulaes below are provided for your convenience.
"µ
#
¶(nY )
APR
1+
−1
n
µ
¶
Saving Plan Formula:
A = PMT ×
APR
µ
¶n
APR
P×
n
Loan Payment Formula: PMT = "
µ
¶(−nY ) #
APR
1− 1+
n
Part I: Basic problems
1. (10 points) If you deposit $7,000 now and you can get an APR of 5% compounded continuously,
how much will you have in 23 years?
2. (10 points) A saving account pays an annual percentage rate of 2.5% compounded quarterly. Find
the annual percentage yield on this account.
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3. (10 points) Life expectancy in 1910 was 35 years and life expectancy in 2008 is 66.12 years. Suppose
it grows linearly, find the rate of change of life expectancy.
4. (10 points) If the US population grows 3.5% per 5 years, estimate the doubling time of it. (Logarithm
is NOT allowed)
5. (10 points) A community of mice has doubling time of 5 months. If there are initially 500 mice,
find the population after 2 years.
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Part II: Advanced problems
6. (10 points) A saving account pays an annual percentage rate of 2.5% compounded quarterly. You
decide that you would like to make a regular quarterly deposits to this account since you would
like to have $750,000 when you retire in 40 years. How much should your quarterly deposits be in
order to accomplish your goal?
7. You have found that you are eligible for a 30-year house loan with annual interest rate (APR) of
6.25%, compounded monthly.
(a) (3 points) If you take out this loan for $200,000, what will your monthly payment be?
(b) (3 points) How much will you pay in interest (in $ terms) over the life of the loan if you take
out this loan for $200,000?
(c) (4 points) If you decide instead to get a 20-year loan at the same rate for the same amount,
what would your monthly payment be and how much would you save (in dollars) in interest
(if you decided to take a 20-year loan instead of 30-year loan).
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8. One morning, there were 3 inches of snow on the ground. Then the winter storm started and snow
started accumulating at a constant rate of 5 inches every 2 hours.
(a) (2 points) Identify the independent and dependent variables.
(b) (5 points) Write a linear equation that describes this situation. Explain the meaning of each
variable in your equation. Draw a graph for this equation.
(c) (3 points) How long did it take for the height of the snow to reach 21 inches?
9. I deposit $1,000 into my saving account and expect that the compound interest would lead me to a
millionaire automatically. Suppose my account has an APR of 5.4% and the interest is compounded
annually.
(a) (5 points) Find the exact doubling time of the accumulated balance.
(b) (5 points) Suppose I’m 20 years old now. How old will I be when I become a millionaire (of
course, I mean only from this account)?
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10. You take 300mg of a certain medication at 2pm. A lab test done at 6pm shows that you still have
120mg of that medication left in your bloodstream.
(a) (5 points) Assuming the medication decays exponentially, what is the rate of decrease of the
medication in your bloodstream?
(b) (5 points) What is the exact half-life of that medication in your bloodstream?
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