Hi, I want understand more on how change in interest rates affect present value of annuities. From what I understand, if interest rates fall, value of annuities also fall because bond prices rise and hence cost of buying annuities for the company rises. However, when interest rates fall, the denominator in the present value formula falls and PV of annuities will rise. This seems little contradicting
Hi Komal It's worth considering separately what happens for annuities that are already in force and what happens for annuity pricing (ie the rates at which customers can buy a new annuity). If interest rates fall and bond prices rise as you say, then for annuities that are already in force, the value of the company's liabilities will rise (as they are the PV of a fixed annuity amount pa now being discounted at a lower rate of interest). Provided the company has matched its assets and liabilities, the value of both has increased. In terms of pricing, when interest rates fall, the amount of annuity pa that a customer will be offered for a certain amount of single premium will be lower (because of that higher PV of the annuity amount). So hopefully no contradiction
