Jamaica HammondMitchell
Chapter 4 Homework Assignment
1,2 4-7, 10–25
4-1 If Samantha invests $700 today in an account that pays 4 percent interest compounded annually, how
much will she have in her account four years from today?
PV: 700 FV:
I/Y %: 4 Answer: $818.900
N: 4
4–2. Fifteen (15) years ago, your parents purchased an investment for $2,500. If the investment earned 6
percent interest each year, how much is it worth today?
N:15
PV: 2,500 Answer: $ 5,991.4
I/Y: 6
FV:
4–4. Staci invested $950 five years ago. Her investment paid 7.2 percent interest compounded monthly.
Staci’s twin sister Shelli invested $900 at the same time. But Shelli’s investment earned 8 percent interest
compounded quarterly. How much is each investment worth today?
Stacy Shelli
PV: 950 PV: 900
N: 5 x 12: 60 N: 5x4: 20
I/Y %: 7.2 /12 I/Y %: 8/4
Stacy: $1,360.19 Shelli: $ 1,337.35
4–5. What is the present value of $1,500 due in 14 years at a
PV: ?
FV: 1,500
N: 14
I/Y: 5, 10
(a)5 percent interest rate
I/Y%: 5 Answer: $757.60
(b)10 percent rate
I/Y%: 10 Answer: $395
Explain why the present value is lower when the interest rate is higher.
Present value is equal to the value today of a payment made on a future date. The higher the interest rate,
the lower the present value of a given payment.
4–6. Matt is considering the purchase of an investment that will pay him $12,500 in 12 years. If Matt wants
to earn a return equal to 7 percent per year (annual compounding), what is the maximum amount he should
be willing to pay for the investment today?
FV: 12,500
PV:
N: 12 Answer: $5,550.14
I/Y%: 7
4–7. What is the present value (PV) of an investment that will pay $2,500 in five years if the opportunity
cost rate is 9 percent compounded?
FV: 2,500
N: 5
I/Y%: 9
(a)annually, I/Y: 1
Answer PV: $ 1,624,82
(b)quarterly, I/Y: 4 N: 20
Answer: PV: $1602,04
(c)monthly, N:5×12: 60
Answer: PV: $1,596.74
Explain why the PV is lowest when interest is compounded monthly.
The frequency of compounding affects the future and present values of cash flows. The longer your time
frame, the less you need to invest today. Alternatively, shorter time periods require larger initial
investments.
4–10. At the end of each of the past 14 years, Vanessa deposited $450 in an account that earned 8 percent
compounded annually.
o (a)How much is in the account today?
a) FV: PV x (1 + Interest Rate) # years – 1
Interest Rate
FV: 450 x (1 + 0.08)14 – 1: $10,896.71
0.08
Answer: FV: $10,896.71
o (b)How much would be in the account if the deposits were made at the beginning each
year rather than at the end of each year?
