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8. Peter joins a saving plan for buying a villa. At the beginning of the first year, Peter deposits an initial amount of $P. At the beginning of each subsequent year, he deposits 21% more than the previous year. The interest rate of the bank is 10% per annum, compounded yearly. (a) Show that the amount in his account at the end of the nth year since the start of the saving plan is $10P (1.1" ) (1.1" -1). (3 marks) (b) It is given that the initial deposit is $125 000. The value of a villa is $(7.25(1.1" ) +1)106 at the end of the nth year since the start of the saving plan. Find the least integral value of n such that the amount in Peter's account is greater than the value of the villa. (4 marks)