Question

Suppose the interest rate is 5% today and will stay constant for exactly 1 year at which time it will increase to 7% for exactly 1 year.  How much would you pay today for a bond that pays you $1378 in exactly 1 year from today and $2345 in exactly 2 years from today?  Support your response

Answer 1

In order to determine what value should be payed for the bond we have to determine the present value of all future receiving from the bond.

Present Value(PV) of amount received after n years is given by :

PV = A/(1 + r)ⁿ

where A = Amount after n years , r = interest rate and n = time and PV = Present value

So Value of amount received in year 2 at Year 1 is given by :

PV = A/(1 + r)ⁿ

where A = Amount after 1 years(Note we are considering value of year 2 at year 1 not at year 0 and that's why n = 1) = 2345 , r = interest rate in for second year = 7% = 0.07 and n = time = 1 and P = Value of amount received at year 2 in year 1.

=> P = 2345/(1 + 0.07)¹ = 2191.59

So Value of total receiving at year 1 = Amount received at year 1 + value of amount received in year 2 at Year 1

= 1378 + 2191.59

= 3569.59

Now Present value of Total amount at Year 1 is given by(Now we have to calculate Net value received in Year 1 at Year 0) :

PV = A/(1 + r)ⁿ

where A = 3569.59 , r = interest rate for first year = 5% = 0.05 and n = time = 1 and PV = Net Present Value

=> PV = 3569.59/(1 + 0.05)

=> PV = 3399.61.

Thus, Value that one will be willing to pay is this Net Present Value.

Hence, Amount one would pay today for this bond is 3399.61