Question

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?
0.05
0.5
1.05
5.0

Answer 1

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...

Answer 2

Answer:

• Every Concecutive Month there is increament of 5% from previous month.

Let the Previous Month Saving be 100.

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$:\implies\tt Next\:Month=Previous\: Month \times (100+Increment)\%\\\\\\:\implies\tt Next\:Month = 100 \times (100 + 5)\%\\\\\\:\implies\tt Next\:Month = 100 \times 105\%\\\\\\:\implies\tt Next\:Month = 100 \times \dfrac{105}{100}\\\\\\:\implies\tt Next\:Month = 105$

$\rule{160}{1}$

$\underline{\bigstar\:\:\textsf{Common Ratio will be Given By :}}$

$\dashrightarrow\tt\:\: Common\:Ratio=\dfrac{a_n+1}{a_n}\\\\\\\dashrightarrow\tt\:\:Common\:Ratio=\dfrac{Next\:Month}{Previous\: Month}\\\\\\\dashrightarrow\tt\:\:Common\:Ratio=\dfrac{105}{100}\\\\\\\dashrightarrow\:\:\underline{\boxed{\textsf{\textbf{Common Ratio = 1.05}}}}$

⠀

$\therefore\:\underline{\textsf{Yuvi should use c) \textbf{1.05} as common ratio}}.$