Why am I getting wrong answer for a problem from simple interest?

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Problem :
The simple interest(S.I) rate offered by a bank is 4% in the first year.
Staring from the second year, the simple interest rate offered by the bank is 1% more than the simple interest rate offered by the bank in the previous year.
After how many years will the total simple interest earned on the deposit be 30% more than the initial amount deposited?

My Solution:
S.I = PNR/100
For 1st year, S.I = P*1*4/100
For 2nd year, S.I = P*1*5/100
For 3rd year, S.I = P*1*6/100
.
.
.
For 13th year, S.I = P*1*16/100

Adding up all the S.I amounts from 1st year to 13th year gives 130*P/100 which is 30% more than P.

Hence the answer should be 13 according to me.

But the given answer is 16.

Can anyone help please?