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19. In June, Cory begins to save money for a video game and a TV he wants to buy in Decembe
He starts with $24. Each month he plans to save 10% more than the previous month. How
much money will he have at the end of December?
O$203.74
O$177.34
O$227.69
O$185.22

Sagot :

adioabiola

The amount of money that he should have at the closing of December should be $235.96

How to find total savings

Given that,

  • Starting amount = $24

And, it plans to save 10% more as compared to the last month.

June =$24

July =24 + 2.4 = $26.4

August = 26.4 + 2.64 =$29.04

September = 29.04 + 2?904 = $31.944

October =31.944 + 3.1944 =$35.0984

November =35.0984 + 3.50984 =$42.60824

December = 42.60824 + 4.260824 =$46.869064

Total savings = 24 + 26.4 + 29.04 + 31.944 + 35.0984 + 42.60824 + 46.869064

= $235.959704

Approximately, $235.96

Learn more about equation:

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sqdancefan

Answer:

  (c)  $227.69

Step-by-step explanation:

The amounts Cory will be adding to his account comprise a geometric series with first term $24 and each successive term 10% more, or 1.10 times the previous term. The total amount Cory will have saved by the end of December is the sum of 7 terms of the series.

__

sum of geometric series

The sum of ...

  24 +1.10×24 +1.10²×24 +... +1.10⁶×24

is given by the formula ...

  Sn = a1×(r^n -1)/(r -1)

where a1 is the first term (24), and r is the common ratio (1.10).

formula application

For the series representing Cory's deposits, we have ...

  S7 = 24×(1.10^7 -1)/(1.10 -1) = 24×0.948717/0.10 ≈ 227.69

At the end of December, Cory will have about $227.69.

_____

Additional comment

A financial calculator or app can also tell you the value of an annuity with a 10% increase per period.

View image sqdancefan
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