Question

What is “discounting,” and how is it related to compounding? How is the future value equation related to the present value equation? How does the present value of a future payment change as the time to receipt is lengthened? As the interest rate increases? Using your results to address these questions. Suppose a risk-free bond promises to pay $2,249.73 in 3 years. If the going risk-free interest rate is 4%, how much is the bond worth today? ($2,000) How much is the bond worth if it matures in 5 rather than 3 years? If the risk-free interest rate is 6% rather than 4%, how much is the 5-year bond worth today? How much would $1 million due in 100 years be worth today if the discount rate were 5%? What if the discount rate were 20%?

Answer 1

Discounting is the process of determining present value of future cash flows and compounding is the process of calculating future value of present value. So, relation between discounting and compounding is that discounting process used to calculate present value and compounding is using to calculate future value.

Discounting and compounding process constitutes three components, Interest rate, tenure of investment and principle value. if either of three factors increase in future value increase and if either of three components decrease in present value increase.

a.

Price of Bond = $2,249.73 / (1 + 4%) ^ 3

= $2,249.73 / 1.1249

= $2,000

Price of bond that is present value of bond is $2,000.

b.

Present worth of bond = $2,249.73 / (1 + 6%) ^ 5

= $2,249.73 / 1.3382

= $1,681.13

Price of bond that is present value of bond is $1,681.13.

c.

if discount rate is 5%.

Present value = $1,000,000 / (1 + 5%) ^ 100

= $1,000,000 / 131.50

= $7,604.49.

Present value is $7,604.49.

again

if discount rate is 20%.

Present value = $1,000,000 / (1 + 20%) ^ 100

= $1,000,000 / 82,817,974.52

= $0.012

Present value is $0.012.