Suppose a Certain Amount of Money Is Deposited into an Account

question 32

Essay

Suppose a certain amount of money is deposited into an account paying $4 \%$ annual interest, compounded quarterly (i.e., four times a year). For each positive integer $n$ , let $S _ { n } =$ the amount on deposit at the end of the $n$ th quarter, and let $S _ { 0 }$ be the initial amount deposited.
(a) Find a recurrence relation for $S _ { 0 } , S _ { 1 } , S _ { 2 } , \ldots$ , assuming no additional deposits or withdrawals for a 3-year period.
(b) If $S _ { 0 } = \$ 5000$ , find the amount of money on deposit at the end of three years.
(c) Find the APR for the account.

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Definitions:

Skewed Distribution

A type of distribution in which data points are not symmetrically distributed around the mean, typically tilting to the left (negatively skewed) or to the right (positively skewed).

Deviations

Differences between observed values and the average of those values, indicating the spread of a dataset.

Observations

Data collected or measured from a study or experiment, representing individual points of information gathered.

Average Score

The term "average score" refers to the mean score obtained by dividing the total sum of all scores by the number of scores.