Maths Question (Interest Rates)

(b) A perpetuity is an investment that pays out a fixed amount at the end of each year forever.
A bank offers an interest rate of 5% per annum with annual compounding.
(i) At the start of 2021, £P is invested in the bank so that a perpetuity of £100 per year will be
paid starting at the end of 2021.
What is the present value of this perpetuity? What is P ?
(ii) A return on an investment is deemed worthless when its present value is less than £1.
What is the first individual payment from the perpetuity in (i) to be deemed worthless?
What is the first payment from the perpetuity in (i) from which all remaining payments will
be deemed worthless?

Could you please answer these two questions?

Reply 1

RichE

Original post by Ahchy

People on this forum don't just give answers out - they need to know you've attempted the problem yourself.
And I'm not even sure this question is answerable (unless there was more information in part (a)). It doesn't seem to provide enough detail. To answer (i) I would guess the interest gained is being used to pay the perpetuity - if you don't assume this you can't answer the question. But that assumption means (ii) is nonsensical.