$\backslash$table$[[$Principal Payment,Amount,Payment Frequency,$\backslash$table$[[$Compounding$],[$Frequency$]],\backslash$table$[[$Interest Rate $($per$],[$annum$)]],$Number of Payments$],[$$$2000,$$$100,12,12,0\mathrm{.}08,],[$$$$4000,$$$100,12,12,0\mathrm{.}08,],[$$$$000,$$$100,12,12,0\mathrm{.}08,],[$$$8000,$$$100,12,12,0\mathrm{.}08,],[10000,$$$100,12,12,0\mathrm{.}08,]]$

a$.$ Does the number of payments increase by the same amount each time? Explain.

b$.$ If the amount of the loan doubles, does the number of payments also double? Explain.

c$.$ Summarize the effect of changing the principal on the number of payments required to pay back a loan when all other conditions remain the same.

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