April 3, 2019

B-58 SOLUTIONS

Solutions to Questions and Problems

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple

steps. Due to space and readability constraints, when these intermediate steps are included in this

solutions manual, rounding may appear to have occurred. However, the final answer for each problem is

found without rounding during any step in the problem.

Basic

1. The simple interest per year is:

So after 10 years you will have:

The total balance will be $5,000 + 4,000 = $9,000

With compound interest we use the future value formula:

The difference is:

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

FV = PV(1 + r)t

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

PV = FV / (1 + r)t

CHAPTER 5 B-59

4. 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

5. 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)

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:

B-60 SOLUTIONS

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)

The length of time to double your money is:

The length of time to quadruple your money is:

Notice that the length of time to quadruple your money is twice as long as the time needed to double

your money (the difference in these answers is due to rounding). This is an important concept of time

value of money.

8. 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:

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:

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