Asap math I need hlp

Question

I have a loan and the interest rate on the loan doubles.

I wish to keep the same amortization period, but should I  double the payment?

If you answer could you please provide an example so I could further understand your reasoning!

Answer 1

A = P i [ (1+i)ⁿ ] / ((1+i)ⁿ - 1]

P stays the same. If i doubles does A double is the question.

Write q = (1 + i)ⁿ

Obviously q > 1 as i > 0 so 1+i > 1, and n >=1.

Then A = Pi [ q / [q-1]]

q / q-1 > q / q = 1 (properties of fraction)

so A = Pi [ q/q-1] > Pi

So A > Pi

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P is constant . If A=Pi then if we doubled i then we would double A

but as A > Pi if we double i the payment will more than double [ reason we have compounded interest here ]

Answer 2

Doubling an Interest Rate, the Regular Payment less than doubles