MATH 1030-008: EXAM 2
Name:
Directions: Please write legibly and circle your final answers. There
are problems on both sides of this paper!!!!
Compound interest formula for continuous compounding:
A = P × e(AP R×Y )
APY
relative increase =
absolute increase
starting principal
Savings plan formula:
h
A = PMT ×
1+
AP R (nY )
n
AP R
n
−1
i
Loan payment formula:
P × APn R
PMT = h
(−nY ) i
1 − 1 + APn R
Approximate Doubling Time and Halving Time formulas:
Tdouble ≈ 70
P
Thalf ≈ 70
P
Equations for Exponential functions
Q = Q0 × (1 + r)t
Q = Q0 × 2t/Tdouble
t/Tdouble
Q = Q0 × 12
1. A bank offers an APR of 5.8%. You deposit $3000 one time.
(a) Find the accumulated balance after one year if compounding occurs quarterly.
(b) Calculate the APY.
(c) How much will your accumulated balance be in 20 years?
2. At age 28 you start saving for retirement. If your investment plan pays an APR of 4.5% and you
want to have $2 million when you retire in 37 years, how much should you deposit monthly?
3. You want to buy a house and the bank has approved you for a 30-year mortgage loan of $150, 000
with an APR of 6.75%, compounded monthly.
(a) What will your monthly payment be?
(b) How much will you pay in interest over the life of the loan?
(c) If you decide instead to get a 15-year loan at the same rate for the same amount, what would
your monthly payment be and how much would you save in interest over the 30-year loan interest
cost?
4. The value of your house is increasing by 8% per year.
(a) What is the approximate doubling time for the value of the house?
(b) If it is worth $100, 000 today, what will it be worth in five years?
5. The cost of renting a car is a flat $35, plus an additional 8 cents per mile that you drive.
(a) Identify the independent variable and dependent variables:
independent variable
dependent variable
(b) Write a linear equation that describes this situation.
(c) How far can you drive for $100?
6. The half-life of aspirin in your blood stream is 3.1 hours.
(a) What percent does it decrease by per hour (i.e., what is the rate of decay)?
(b) If you take 2 aspirin (650 mg total) at 8 o’clock in the morning, at what time should you take
a second dose? (Assume that you take the second dose when your headache returns - when there is
only 100 mg left in your bloodstream.)
Extra Credit
Derive the exact formulas for doubling time and half-life time, Tdouble and Thalf respectively, using the
general exponential function.