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Yui makes a list of the balances in her savings account at the end of each month. She notices that each month’s total is 5% greater than the previous month’s total. She writes a recursive formula to describe the account balances.Which value should she use as the common ratio?0.050.51.055.0 |
Answer» Solution :-Let us Assume That, her saving at the END of first month is Rs.X . Now, in Next Month his saving is 5% greater than the PREVIOUS month’s TOTAL saving . So, → Yui , Saving after End of second Month = Previous Month Saving + (5% of Previous Month Saving) = x + (5 % of x ) = x + (5*x/100) = x + 0.05x = 1.05x. So, Yui Salary is 1.05 times of Previous Month salary. _________________Now, Lets Check Further also , → Saving after End of Second Month = 1.05x . → Saving after end of Third month = Saving after end of second month + (5% of Saving after end of second month) = 1.05x + (5% of 1.05x) = 1.05x + [ ( 5 * 1.05x)/100 ] = 1.05x + 0.05 * 1.05x = 1.05x ( 1 + 0.05) = 1.05x * 1.05. Hence, we can conclude That, Each month we have to multiply the previous AMOUNT with 1.05... |
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