Question

X

In June, Cory begins to save money for a video game and a TV he wants to buy in December. 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?
A. $203.74
B. $177.34
C. $227.69
D. $185.22

Answer 1

$185.17

Explanation:

The monthly dollar amounts saved here form a geometric progression, since each new amount is derived by multiplying the previous amount by 1.10. This 1.10 is r, the common ratio. The first term is $24 and there will be 5 more terms (June through December is 6 months).

The general formula for individual terms of a geometric series is A(n) = A(1) + r^(n - 1).

Here, with A(1) = $24 (the first term), r =1.10 and n = 6, we'd get $38.65 (the 6th and last term). Following the same procedure, we'd find that the 6 terms will have the values $24, $26.40, $29.04, $31.94, $35.14. $38.65.

Finally, we add these up. We get the sum $185.17.

Fortunately, there's a formula that makes the calculations go much faster: "sum of a geometric sequence." This formula is:

1 - r ^n

a(1)*--------------

1 - r

Here, a(1) = $24 and r = 1.10, and so the sum of the first 6 terms of this geometric sequence is

1 - 1.10^6

$24*---------------- = $185.17

1 - 1.10