please do not use excel

A loan of $$1\mathrm{.}000$ is to be repaid by annual installments at the end of each year for $21$ years using the following schedule:

In years $1$ through $10,$ the installment is $$50.$ In years $11$ through $20,$ the installment is $$100.$

In year $21,$ the installment equals the balance amount required to liquidate the loan. Interest is at a $5\%$ annual effective rate.

Determine in which of the following ranges does the amount of principal included in the $12$th instaliment lie