Ms. Smith takes out an endowment policy with an insurance company which involves making a fixed payment of $ P each year. At the end of n years, Ms. Smith expects to receive a payout of a sum of money which is equal to her total payment together with interest added at the rate of x % per annum of the total sum in the fund.

(a) Show that the total sum in the fund at the end of the second year is $P (R+R^2) , where

R = (1+ x /100 )

.

(b) Show, by making a valid argument, that the total sum in the fund at the end of the nth year is given by

$PR (R^n - 1) / R-1

(c)Find the value of P, to the NEAREST dollar, when n = 10, x = 8 and the payout is 1.5 million.