1. Solve each equation.
(a) e6x = 4e12
(b) log2 (x − 1) + log2 (x − 2) = log2 3 − 2
2. A certain warren contains 12 rabbits. The population doubles every three days.
(a) How many rabbits are there after 0 days? How many after 3 days?
(b) Use your answers above to write an equation of the form y = aekt giving the
number of rabbits in the warren after t days.
(c) After how long will there be 2000 rabbits?
(d) How many rabbits will there be after 40 days?
Page 2
3. We learned formulas describing the following financial ideas:
• Simple interest
• Periodically compounded interest
• Continuously compounded interest
• APY of an account
• Future value of an annuity due
• Future value of an ordinary annuity
• Sinking fund
• Present value of an ordinary annuity
• Present value of an annuity due
• Present value of a deferred annuity
• Periodic payment of an amortized loan
• Total interest paid
• Loan payoff amount
Decide which formula should be used to solve each problem below. (You don’t need to
solve the problem. Just decide which formula applies.)
(a) A bank robber has stolen $20,000 which he places in an account (at a different
bank) paying 7.5% interest compounded quarterly. He intends to make equal
withdrawals at the beginning of each quarter for 15 years. How much will each
withdrawal be?
(b) Which of the following accounts pays best?
i.
ii.
iii.
iv.
7.5% compounded annually
7.25% compounded quarterly
7% compounded monthly
7.75% compounded continuously
(c) Martha Stewart wants to redo her kitchen. Her standards are high, so this will
cost her $1,200,000. She doesn’t want to take out a loan, so instead she decides to
save up, making monthly deposits in an account paying 11% interest compounded
monthly. If she intends to save for three years, how much does each payment need
to be?
Page 3
(d) Paula Dean also wants to redo her kitchen. Her wants are more modest, so
she intends to spend only $800,000. She will take out a loan at 12.7% interest
compounded quarterly and pay it back in quarterly payments over 5 years. How
much will each payment be?
(e) Robert has very little financial experience, so he deposits his $8000 in savings in
an account paying 7.5% simple interest. How much money will Robert have 15
years from now?
(f) Kelly is saving for retirement. She pays $400 at the end of each month into an
account paying 8.2% interest compounded monthly. If she retires in 35 years, how
much money will she have?
(g) How much money should be invested at 6% interest compounded continuously to
have a total of $12,000 after 10 years?
(h) George took out a loan of $60,000 to pay for school. The interest is 3.8% compounded monthly. George intended to pay off the loan in twenty years, but after
eight years of payments he received an inheritance allowing him to pay off the
rest in a lump. How much money was required to make this payment?
(i) Allen wins the lottery. He expects a lump payment of $2,000,000, but he discovers
that his prize will be paid out in installments of $25,000 at the end of each
quarter for the next 20 years. If the money is in an account paying 6% interest
compounded quarterly, what is the current value of the account?
(j) Carrie takes out a mortgage for $250,000 at an interest rate of 6.3% compounded
monthly for twenty years. If Carrie makes equal monthly payments on the loan,
what is the total finance charge?
(k) Horatio wants to buy a yacht. If he puts $500 at the beginning of each month
into an account paying 7.2% interest compounded monthly for the next ten years,
how much can he spend on his yacht?
(l) Joan invests $15,000 in an account paying 7% interest. How much money will she
have in 15 years?
(m) Hugo sets up a college fund for his newborn baby, Genevieve. Hugo will put a
lump sum into an account paying 8.8% interest. When Genevieve turns 18, she
Page 4
will make regular withdrawals of $3,000 at the beginning of each month for four
years. How much does Hugo need to invest now?
Page 5