April 3, 2019

CHAPTER 5 B-61

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

PV = FV / (1 + r)t

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

FV = PV(1 + r)t

13. 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

To find the FV of the first prize, we use:

FV = PV(1 + r)t

14. 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

15. 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

Notice that the interest rate is negative. This occurs when the FV is less than the PV.

B-62 SOLUTIONS

Intermediate

16. 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

a. PV = $100,000 / (1 + r)30 = $24,099

b. PV = $38,260 / (1 + r)12 = $24,099

c. PV = $100,000 / (1 + r)18 = $38,260

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

PV = FV / (1 + r)t

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

FV = PV(1 + r)t

Better start early!

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

CHAPTER 5 B-63

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

Solving for t, we get:

So, the money must be invested for 19.31 years. However, you will not receive the money for

another two years. From now, you’ll wait:

Calculator Solutions

1.

Enter 10 8% $5,000

N I/Y PV PMT FV

2.

Enter 11 10% $2,250

N I/Y PV PMT FV

Enter 7 8% $8,752

N I/Y PV PMT FV

Enter 14 17% $76,355

N I/Y PV PMT FV

Enter 8 7% $183,796

N I/Y PV PMT FV

3.

Enter 6 7% $15,451

N I/Y PV PMT FV