Question

1. Suppose you save $18,000 per year at an interest rate of i= 5.21% compounded annually. How much will you have after 35 years?

2. A risk-free bond will pay you $1,000 in 1 year. The annual discount rate is i= 3.69% compounded annually. What is the bond's present value?

3. A risk-free bond will pay you $1,000 in 2 years and nothing in between. The annual discount rate is i= 9.5% compounded annually. What is the bond's present value?

Answer 1

1) Here Annuity = 18000$ , n = no of years = 35 , r = interest rate = 5.21%

FV(annuity) = Annuity[(1+r)^n - 1 /r ]

= 18000[(1+5.21%)^35 - 1 / 5.21%]

= 18000[(1.0521)^35 - 1 / 5.21%]

= 18000[5.9156 - 1 / 0.0521]

= 18000[4.9156/0.0521]

= 18000[94.3485]

= 16,98,273.42 $

Thus one will have $ 1698273.42 after 35 years

2) Here FV = 1000$ , n = no of years = 1 , r = rate of interest = 3.69%

PV = FV/(1+r)^n

= 1000/(1+3.69%)^1

= 1000/(1.0369)^1

= 964.41 $

Thus present value of bond = 964.41 $

3)

Here FV = 1000$ , n = no of years = 2 , r = rate of interest = 9.5%

PV = FV/(1+r)^n

= 1000/(1+9.5%)^2

= 1000/(1.095)^2

=1000/1.199025

= 834.01 $

Thus present value of bond = 834.01 $