Jasper takes out a loan of $100,000$ at an effective rate of $7\%.$ He will repay the loan with payments at the end of each year for $25$ years. His first payment will be X and each subsequent payment will increase by $4\%.$

Calculate the principal repaid in the $16$th payment.

A

$4,486$

B

$5,398$

C

$5,552$

D

$2,997$

E

$6,512$