Question

Suppose you paid $1,000 for a perpetuity bond that pays $40 a year. Suppose the interest rate drop fall to 1%. What would be the price of the bond if it continues to pay $40 per year?

Answer 1

PV=1,333

Step-by-step explanation:

the key to answer this question is to remember the formula for calculating a perpetuity:

`PV=(C)/(i)`

where PV is the present value, C is the regular payment and i is the interest rate charged, so in the initial case we have:

`1,000=(40)/(i)`

solving i we have:

i=40/1,000

i=0.04

so if the i rate falls 1 % the price of the bond will be

`PV=(40)/(0.03)`

`PV=1,333`

it could sound rare that if the rate falls the present value increases but keep in mind that the more rate the less price is a relation between rates and bonds prices