Question

If the APR is 4% and the compounding period is monthly, what is the EAR?

2.Would you prefer $1000 today or $2000 in 5 years?

a.If the prevailing interest rate is 9%

b.If the prevailing interest rate is 18%

3What is the present value of a perpetuity that pays an annual cash flow of $150 with prevailing interest rates of 5%?

4What is the present value of a perpetuity that pays its first cash flow of $500 one year from now and then grows by 3% per year. Assume prevailing interest rates of 6%?

Answer 1

a)

EAR = ( 1 + 0.04 / 4)⁴ - 1

EAR = ( 1 + 0.01)⁴ - 1

EAR = 1.040604 -1 = 4.0604%

b)

Present value of 2000 if interest rate is 9%

PV = 2000 / ( 1 + 0.09)⁵

PV = 1299.86

I would prefer 2000 in 5 years since it's present value is greater than 1000

Present value of 2000 if interest rate is 18%:

PV = 2000 / ( 1 + 0.18)⁵

PV = 874.21

I would prefer 1000 today since the present value of 2000 is less than 1000

c)

Present value of perpetuity = 150 / 0.05

PV = 3000

d)

Present value = cash flow / rate - growth

Present value = 500 / ( 0.06 - 0.03)

Present value = 16,666.67