sg578144
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a bank received an initial deposit of $9000 kept a percentage of this money in reserve based on a reserved rate of 9% and loaned out the rest. the amount it loaned out all was eventually deposited back into the bank. if the cycle continued, how much eventually resulted from the initial deposit?

Respuesta :

Aliwohaish12
Hi there

The answer is
9,000÷0.09
=100,000

Hope it helps

Answer:

100000

Step-by-step explanation:

Given that  a bank received an initial deposit of $9000 kept a percentage of this money in reserve based on a reserved rate of 9%

Initial deposit -9000

Loan amount - 91% of 9000 = 8190

This loan amount would be deposited and hence

total deposit available =9000+8190=17190

Now initial deposit became 191%

Loan would be 91% of 8190

This would be deposited again

Thus deposit increase in geometric progression with common ratio as 0.91

This would be an infinite series with common ratio =0.91<1

Hence total deposits would be

=sum of infinite series

= [tex]\frac{9000}{1-0.91} =\frac{9000}{0.09} \\=100000[/tex]

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