5. When interest is compounded, the interest earned is added to the principal amount sothat it may also earn interest. For a 1-year period, the principal amount Q is given byniQ = (₁ + ²+ )"nQ (0)where i is the annual interest rate (given as a decimal) and n is the number of timesduring the year that the interest is compounded.Modeling with a Differential Equationtights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).sed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.To lure depositors, banks offer to compound interest at different intervals: semi-annually, quarterly, or daily. A certain bank advertises that it compounds interest con-tinuously. If $100 is deposited initially, formulate a mathematical model describing thegrowth of the initial deposit during the first year. Assume an annual interest rate of 10%.

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Modeling with a Differential Equation To lure depositors, banks offer to compound interest at different intervals: semi- annually, quarterly, or daily. A certain bank advertises that it compounds interest con- tinuously. If $100 is deposited initially, formulate a mathematical model describing the growth of the initial deposit during the first year. Assume an annual interest rate of 10%.