February 27
Name:
Compound interest:
APR
A=P × 1+
n
n×Y
Savings plan:
P×
A=
h
1+
APR
n
APR
n
n×Y
i
−1
Problems 1 - 7 : Choose the best answer to each of the following questions. Explain your
reasoning with one or more complete sentences.
1. (3 pts) A negative monthly cash flow means that
b) you are spending more money than you are taking in.
Cash flow = money in - money out, is negative when money out is larger.
2. (3 pts) Alice smokes about 1 12 packs of cigarettes per day and pays about $6.60 per
pack. Her monthly spending on cigarettes is closet to
c. Ans 30 days = 1 month: 1.5 × 6.6 × 30 = $297.
3. (3 pts) Bob goes to a club or concert every two weeks and spends an average of $60
each time. His annual spending is closest to
a. Ans 12 months = 1 year: 60 ∗ 2 ∗ 12 = $1440.
c. Ans 52 weeks = 1 year: 60 ∗ 26 = $1560.
4. (3 pts) With the same deposit, APR, and length of time, an account with monthly
compounding yields
c. a greater balance than an account with annual compounding.
With annual compounding, APR = APY. With monthly compounding, APR ¡ APY.
5. (3 pts) A bank account with compound interest exhibits what we call
c. exponential growth.
It grows as a percentage change over time.
6. (3 pts) In the savings plan formula, assuming all other variables are constant, the
accumulated balance in the savings account
c. increases as Y increases.
Longer saving terms (bigger Y ) yeilds larger savings.
7. (3 pts) Suppose you deposit $100 per month into a savings plan for 10 years, and at
the end of that period your balance was $32,200. The amount you earned in interest
was
b. $20,200
100 × 12 × 10 = $12000 is the total deposits. $32, 000 − $12, 000 = $20, 200 gained
in interest.
8. (2 pts) If you deposit $2,000 now at an APR of 5% compounded monthly, how much
will you have in 15 years? Round to the nearest whole dollar.
0.05
A = 2000 × 1 +
12
12×15
= $4227
9. (2 pts) A bank offers an APR of 4.2% compounded monthly. Find the annual
percentage yield (APY) to the nearest 0.01%.
(1 + 0.042/12)12 = 1.0428 Then APY = 4.28%.
10. (2 pts) Find the savings plan balance after 3 years with an APR of 4% and monthly
payments of $400. Assume monthly compounding, and round to the nearest whole
dollar.
400 ×
A=
h
1+
0.04
12
0.04
12
12×3
i
−1
= $134973