Chapter 5
Questions and Problems
• 1. Simple Interest versus Compound Interest
• Bandung Bank pays 7 percent simple interest on
its savings account balances, whereas Surabaya
Bank pays 7 percent interest compounded
annually. If you made a 20,000 baht deposit in
each bank, how much more money would you
earn from your Surabaya Bank account at the
end of 10 years?
• 1.
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The simple interest per year is:
฿20,000 × .07 = ฿1,400
So after 10 years you will have:
฿1,400 × 10 = ฿14,000 in interest.
The total balance will be ฿20,000 + 14,000 = ฿34,000
With compound interest we use the future value formula:
FV = PV(1 +r)t
FV = ฿20,000(1.07)10 = ฿39,343.03
The difference is:
฿39,343.03 – 34,000 = ฿5,343.03
• 6. Calculating Interest Rates
• Assume the total cost of a college
education in Singapore will be SGD
250,000 when your child enters college in
18 years. You presently have SGD 43,000
to invest. What annual rate of interest
must you earn on your investment to cover
the cost of your child's college education?
• 6.
• To answer this question, we can use either the
FV or the PV formula. Both will give the same
answer since they are the inverse of each other.
We will use the FV formula, that is:
• FV = PV(1 + r)t
• Solving for r, we get:
• r = (FV / PV) 1 / t – 1
• r = (SGD 250,000 / SGD 43,000)1/18 – 1 =
10.27%
• 7. Calculating the Number of Periods
• At 9 percent interest, how long does it take
to double your money? To quadruple it?
• 7.
• To find the length of time for money to double, triple, etc.,
the present value and future value are irrelevant as long
as the future value is twice the present value for doubling,
three times as large for tripling, etc. To answer this
question, we can use either the FV or the PV formula.
Both will give the same answer since they are the
inverse of each other. We will use the FV formula, that is:
• FV = PV(1 + r)t
• Solving for t, we get:
• t = ln(FV / PV) / ln(1 + r)
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The length of time to double your money is:
FV = $2 = $1(1.09)t
t = ln 2 / ln 1.09 = 8.04 years
The length of time to quadruple your
money is:
• FV = $4 = $1(1.09)t
• t = ln 4 / ln 1.09 = 16.09 years
• 9. Calculating the Number of Periods
• You're trying to save to buy a new
€150,000 Fen-art. You have €40,000 today
that can be invested at your bank. The
bank pays 4 percent annual interest on its
accounts. How long will it be before you
have enough to buy the car?
• 9. To answer this question, we can use either
the FV or the PV formula. Both will give the
same answer since they are the inverse of each
other. We will use the FV formula, that is:
• FV = PV(1 + r)t
• Solving for t, we get:
• t = ln(FV / PV) / ln(1 + r)
• t = ln (€150,000 / €40,000) / ln 1.04 = 33.70
years
• 17. Calculating Present Values
• Suppose you are still committed to owning
a €150,000 Ferrari (see Question 9). If you
believe your mutual fund can achieve an
18 percent annual rate of return and you
want to buy the car in 10 years on the day
you turn 30, how much must you invest
today?
• 17.To find the PV of a lump sum, we use:
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PV = FV / (1 + r)t
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PV = €150,000 / (1.18)10 = €28,659.67
• 18. Calculating Future Values
• You have just made your first 250,000 yen
contribution to your retirement account.
Assuming you earn a 10 percent rate of return
and make no additional contributions, what will
your account be worth when you retire in 45
years? What if you wait 10 years before
contributing? (Does this suggest an investment
strategy?)
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18.To find the FV of a lump sum, we use:
FV = PV(1 + r)t
FV = ¥250,000 (1.10)45 = ¥18,222,620.92
FV = ¥250,000 (1.10)35 = ¥7,025,609.21
• Better start early!
• 19. Calculating Future Values
• You are scheduled to receive 402,500
rupees in two years. When you receive it,
you will invest it for six more years at 6.5
percent per year. How much will you have
in eight years?
• 19. We need to find the FV of a lump sum.
However, the money will only be invested
for six years, so the number of periods is
six.
• FV = PV(1 + r)t
• FV = INR 402,500(1.065)6 = INR
587,304.77