1.1.3 The Future Value and Present Value of a Single Cash Flow

Question 1

What is the Formula of Future Value ?

FV = future value at time X
PV = present value
r = interest rate per period
N = number of years

Answer 1

Formula : FV=PV(1+i)^n

Question 2

What is the key assumption of future value formula? (explanation + essentially in 1 word)

Answer 2

A key assumption of the future value formula is that interim interest earned is reinvested at the given interest rate (r).

This is known as compounding.

Question 3

What is the Formula of PV?

N = number of periods
I/Year = yield in market place or the required rate of return
PV = present value
PMT = payment amount per period
FV = the future value of the investment

Answer 3

Formula : PV=FV/(1+i)^n

Question 4

Example 1
An analyst invests $5 million in a 5-year certificate of deposit (CD) at a local financial institution. The CD promises to pay 7% per year compounded annually. The institution also allows him to reinvest the interest at the same CD rate for the duration of the CD. How much will the analyst have at the end of five years if his money remains invested at 7% for five years with no withdrawals of interest?

Answer 4

=PV(1+i)^n
=5000000((1+0.07)^5)
=7012758.654

Question 5

Example 2
An analyst invests $5 million in a 5-year certificate of deposit (CD) at a local financial institution. The CD promises to pay 7% per year, compounded semi-annually. The institution also allows him to reinvest the interest at the same CD rate for the duration of the CD. How much will the analyst have at the end of five years if his money remains invested at 7% for five years with no withdrawals of interest?

Answer 5

=5000000((1+(0.07/2))^(52))

Question 6

1. You anticipate that you will receive $4,500 at the end of 5 years. If you had the money today, it could be invested at a rate of 5% per year. What is the present value of the money?
   A. 3,525.87
   B. 5,743.27
   C. 21,428.57

Answer 6

Correct Answer: A PV = 4500 x (1/1.05)5 = 3525.87

Question 6

1. You anticipate that you will receive $4,500 at the end of 5 years. If you had the money today, it could be invested at a rate of 5% per year. What is the present value of the money?
   A. 3,525.87
   B. 5,743.27
   C. 21,428.57

Answer 6

Correct Answer: A PV = 4500 x (1/1.05)5 = 3525.87

Question 6

1. You anticipate that you will receive $4,500 at the end of 5 years. If you had the money today, it could be invested at a rate of 5% per year. What is the present value of the money?
   A. 3,525.87
   B. 5,743.27
   C. 21,428.57

Answer 6

Correct Answer: A PV = 4500 x (1/1.05)5 = 3525.87

Question 7

2. You have received $125 today. You will invest the money at a rate of 6% per year. How much will your investment have increased by the end of 5 years?
   A. $159.54
   B. $167.28
   C. $167.51

Answer 7

Correct Answer: B FV = (125)(1.06)5 = 167.28

Question 8

3. You expect to receive a lump sum distribution of $285,000 from your pension plan in 18 months. Assuming continuous compounding at an annual rate of 7%, what is the present value of the distribution?
   A. $245,732.88
   B. $256,592.49
   C. $316,549.50

Answer 8

Correct Answer: B In continuous compounding, N is the number of periods of compounding at the per period rate, r. In this case, r=7% per year, and N=1.5 years.

Question 9

4. You have received $350 today. You will invest the money at a rate of 8% per year, compounded quarterly. How much will your investment have increased to by the end of 5 years?
   A. $490.00
   B. $514.26
   C. $520.08

Answer 9

Correct Answer: C FV = ($350) (1.02)20 = $520.08

Question 10

4. You have received $350 today. You will invest the money at a rate of 8% per year, compounded quarterly. How much will your investment have increased to by the end of 5 years?
   A. $490.00
   B. $514.26
   C. $520.08

Answer 10

Correct Answer: C FV = ($350) (1.02)20 = $520.08

Question 11

5. You have $1,000 to invest today. In order for your $1,000 investment to grow to $1,593.85 at the end of 8 years, the money must be invested at what interest rate?
   A. 6%
   B. 7%
   C. 8%

Answer 11

Correct Answer: A Rate = (1593.85/1000)1/8 - 1 = 6%

Question 12

5. You have $1,000 to invest today. In order for your $1,000 investment to grow to $1,593.85 at the end of 8 years, the money must be invested at what interest rate?
   A. 6%
   B. 7%
   C. 8%

Answer 12

Correct Answer: A Rate = (1593.85/1000)1/8 - 1 = 6%

Question 13

5. You have $1,000 to invest today. In order for your $1,000 investment to grow to $1,593.85 at the end of 8 years, the money must be invested at what interest rate?
   A. 6%
   B. 7%
   C. 8%

Answer 13

Correct Answer: A Rate = (1593.85/1000)1/8 - 1 = 6%

Question 14

6. You have a nest egg of $750. In order for your money to grow to $946.88, it must be invested at 6% for how many years?
   A. 3
   B. 4
   C. 5

Answer 14

Correct Answer: B Years = [Log(946.88/750)]/[Log1.06] = 4

Question 15

6. You have a nest egg of $750. In order for your money to grow to $946.88, it must be invested at 6% for how many years?
   A. 3
   B. 4
   C. 5

Answer 15

Correct Answer: B Years = [Log(946.88/750)]/[Log1.06] = 4

Question 16

7. If you are given a present value, the length of time the money is to be invested, compounding interval, and the future value of the investment, you can solve for the interest rate that was earned on the investment. True or False?

Answer 16

Correct Answer: True