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Tju [1.3M]
3 years ago
5

Find the savings plan balance after 2 years with an APR of 4% and monthly payments of $250. The balance is $ (Do not round until

the final answer. Then round to the nearest cent as needed.) Enter your answer in the answer box O Type here to search
Mathematics
1 answer:
alexdok [17]3 years ago
6 0

Answer:

$6,506.51

Step-by-step explanation:

Recall that increasing an amount C in x% is equivalent to multiply it by (1+x/100)

As we have 4% APR, the monthly interest would be (4/12)% = 0.04/12

<u>Month 0</u> (first payment)

$250

Month 1

250 + 250 \frac{0.04}{12}= 250(\frac{12.04}{12})

<u>Month 2</u>

250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2)

<u>Month 3</u>

250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3)

<u>Month 24 (2 years)</u>

250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24})

The sum  

1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24}

is the sum of the first 24 terms of a geometric sequence with common ratio \frac{12.04}{12} which is

\frac{1-(12.04/12)^{25}}{1-(12.04/12)}=26.02603071

so, after 2 years the saving balance is

250*26.02603071 = 6,506.50767= $6,506.51 rounded to the nearest cent.

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