$500 is deposited into an account that pays 5% interest annually at the beginning of the next year. At the end of every year (other than the first), an additional $100 is deposited into the account:

(a) Give the recurrence relation that describes How much money is in the account in the nth year.

(b) Find the closed form representation of this recurrence relation.

(c) Using this closed form representation, give the exact numerical value of the amount in the bank

account at the start of year 8.