Given data : The range of simple interests is between 120$ and 140$(with 10% and 20% interest)
Minimum range(Simple interest difference : 120$)At 10% interest, Amount is 600$ to achieve 120$ over a period of 2 years(60$ * 2)
At 20% interest, For amount = 600$, we will have 240$ interest for 2 years(120$ * 2)
Given the difference in the simple interests will be 120$.
When charging 10% compound interest
For this amount the compound interest will be 60$(for 1st year) and 66$(for 2nd year)
Total Compound interest is 126$
When charging 20% compound interest
For this amount the compound interest will be 120$(for 1st year) and 144$(for 2nd year)
Total Compound interest is 264$
Difference(Compound interest) is 264$ - 126$ = 138$
Maximum range(Simple interest difference : 140$)At 10% interest, Amount : 700$ to achieve 140$ over a period of 2 years(70$ * 2)
At 20% interest, For amount = 700$, we will have 280$ interest for 2 years(140$ * 2)
As given the difference in the simple interests will be 140$.
When charging 10% compound interest
For this amount the compound interest will be 70$(for 1st year) and 77$(for 2nd year)
Total Compound interest is 147$
When charging 20% compound interest
For this amount the compound interest will be 140$(for 1st year) and 168$(for 2nd year)
Total Compound interest is 308$
Difference(Compound interest) is 308$ - 147$ = 161$
Hence, compound interest must be in the range $138 and $161(Option D)
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