Please explain the process of solving this question clearly.

Assume that securitization combined with borrowing and irrational exuberance in Hyperville have driven up the value of existing

financial securities at a geometric rate, specifically from $$6$ to $$12$ to $$24$ to $$48$ to $$96$ to $$192$ over a six$-$year time period. Over the

same period, the value of the assets underlying the securities rose at an arithmetic rate from $$6$ to $$9$ to $$12$ to $$15$ to $$18$ to $$21.$

If these patterns hold for decreases as well as for increases, by how much would the value of the financial securities decline if the

value of the underlying asset suddenly and unexpectedly fell by $$6?$

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Explanation

Assume that securitization combined with borrowing and irrational exuberance in Hyperville have driven up the value of existing financial securities at

a geometric rate, specifically from $$6$ to $$12$ to $$24$ to $$48$ to $$96$ to $$192$ over a $6-$year time period. Over the same period, the value of the assets

underlying the securities rose at an arithmetic rate from $$6$ to $$9$ to $$12$ to $$15$ to $$18$ to $$21.$ Assuming existing ratios, by how much would the value of

the financial securities decline if the value of the underlying asset suddenly and unexpectedly fell by $$6?$

Since we are assuming the same ratios $($or structure of the growth rates remain the same$),$ a decline in underlying asset value by $$6$ results in a new

value of $$15($falls from $$21,$ the current value, to the new value of $$15).$

This implies that value of existing financial securities$,$ which grew at a geometric rate, falls back to $$15.$ This was the existing asset value

with the underlying asset value $5$ years ago $($the underlying asset value was $$15$ five years ago$).$

Thus, the value of the financial securities would fall by $$144.$