Financial

Week 5 (Answers)

Chapter 4 - Questions and Problems

18. To find the FV of a lump sum, we use:

FV = PV(1 + r)t

FV = $5,000(1.1050)45

FV = $446,963.97

If you wait 10 years, the value of your deposit at your retirement will be:

FV = $5,000(1.1050)35

FV = $164,683.37

Better start early!

19. Even though we need to calculate the value in eight years, we will only have the money for six years, so we need to use six years as the number of periods. To find the FV of a lump sum, we use:

FV = PV(1 + r)t

FV = $13,000(1.10)6

FV = $23,030.29

20. 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

$160,000 = $25,000(1.09)t

t = ln($160,000 / $25,000) / ln 1.09

t = 21.54 years

From now, you’ll wait 2 + 21.54 = 23.54 years

22. 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. We also need to be careful about the number of periods. Since the length of the compounding is three months and we have 24 months, there are eight compounding periods. 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 = ($4 / $1)1/8 – 1

r = 0.1892 or 18.92%

23. 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

$4,000 = $1,800(1.0035)t

t = ln($4,000 / $1,800) / ln 1.0035

t = 228.54 months

24. To find the PV of a lump sum, we use:

PV = FV / (1 + r)t

PV =...