*10. Assuming that the force of interest per annum at time t years will be
$$δ_t = (p+s)\frac{rse^{st}}{1+re^{st}}$$
where p,r and s are constants, show that the present value of 1 due at time
T years is
$$\left(\frac{1}{1+r}\right)e^{-(p+s)T} + \left(\frac{r}{1+r}\right)e^{-pt}$$
Hence or otherwise find the present value of a annuity-certain of 1 per annum
payable quarterly in arrear for 10 years when the above formula for δ, holds
with p = 0.09532, r = 2, and s = 0.08701.
[Time estimate 30 minutes]