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Fofino [41]
3 years ago
5

119. Beatrice decides to deposit $100 per month at the end of every month in a bank with an annual interest rate of 5.5% compoun

ded monthly.
a. Write a geometric series to show how much she will accumulate in her account after one year.
Mathematics
1 answer:
sveta [45]3 years ago
3 0

Answer:

Beatrice will accumulate $1230.72 at the end of the year.

Step-by-step explanation:

We can write:

(1+\frac{0.055}{12})=z

100=C for deposits

The first month would have only the deposit reflected in her balance, then, expanding some steps of the calculation would yield:

S_{1}=C\\S_{2}=Cz + C\\S_{3}=Cz^{2}+Cz + C\\S_{n}=Cz^{n-1} +...+Cz+C

A geometric series is given by:

1+x+...+x^{m}=\frac{x^{m+1}-1}{x-1}

Translating our series to the short form:

S_{n}=C(\frac{z^{n}-1}{z-1} )

plugin in the values for the 12 month gives:

S_{12}=100(\frac{(1+\frac{0.055}{12})^{12} -1}{\frac{0.055}{12}})=1230.7169

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