An individual aged 35 exactly deposits each year in arrears an amount in a bank account that pays an effective interest rate of i=2% pa.

The amount deposited in the first year is 10,000, and this amount increases each year at a compound rate of j pa, where j>i.

The last deposit is made at the end of the year of age 64, which means that the total number of deposits is 30.

After the last deposit, the individual starts withdrawing each year in arrears a fixed amount of 30,000, i.e. the first withdrawal is made at the end of the year of age 65.

Assuming that the accumulated value at the end of the year of age 64 of all deposits is equal to 600,000, what is the numerical value of the compound rate j?

All payments are deterministic, and mortality is not taken into account.

Derive an analytical expression of the accumulated value at the end of the year of age 64 of all deposits, i.e. at the time of the last deposit.