Question

10.  Problem 5.10

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PRESENT AND FUTURE VALUES FOR DIFFERENT INTEREST RATES

Find the following values. Compounding/discounting occurs annually. Round your answers to the nearest cent.

a. An initial $300 compounded for 10 years at 9%.

$  

b. An initial $300 compounded for 10 years at 18%.

$  

c. The present value of $300 due in 10 year at 9%.

$  

d. The present value of $2,850 due in 10 years at 18%.

$  

e. The present value of $2,850 due in 10 years at 9%.

$  

Define present value.

1. The present value is the value today of a sum of money to be received in the future and in general is less than the future value.
2. The present value is the value today of a sum of money to be received in the future and in general is greater than the future value.
3. The present value is the value today of a sum of money to be received in the future and in general is equal to the future value.
4. The present value is the value in the future of a sum of money to be received today and in general is less than the future value.
5. The present value is the value in the future of a sum of money to be received today and in general is greater than the future value.

-Select-IIIIIIIVVItem 6

How are present values affected by interest rates?

-Select-Assuming positive interest rates, the present value will increase as the interest rate increases.Assuming positive interest rates, the present value will decrease as the interest rate increases.Assuming positive interest rates, the present value will decrease as the interest rate decreases.Assuming positive interest rates, the present value will not change as the interest rate increases.Assuming positive interest rates, the present value will not change as the interest rate decreases.Item 7

Answer 1

Question 1

This question requires application of basic time value of money, which is:

FV = PV * (1 + r)ⁿ

a) FV = $300 * (1 + 9%)¹⁰

FV = $300 * 2.3674

FV = $710.21

b) FV = $300 * (1 + 18%)¹⁰

FV = $300 * 5.2338

FV = $1,570.15

c) $300 = PV * (1 + 9%)¹⁰

PV = $300/2.3674

PV = $126.72

d) $2850 = PV * (1 + 18%)¹⁰

PV = $2850/5.2338

PV = $544.53

e) $2850 = PV * (1 + 9%)¹⁰

PV = $2850/2.3674

PV = $1203.87

Question 2

Based on definition, correct option is OPTION 1. The present value is the value today of a sum of money to be received in the future and in general is less than the future value.

Question 3

Correct option is: Assuming positive interest rates, the present value will decrease as the interest rate increases.

Based on the time value of money relation above, PV is inversely related to interest rate. So, higher the interest rate, lower the present value.