An account now contains $12,680 and has been accumulating interest at a 8% annual rate, compounded continuously, for 7 years. find the initial deposit. (round your answer to the nearest cent.)

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08-11-2022
Mathematics

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An account now contains $12,680 and has been accumulating interest at a 8% annual rate, compounded continuously, for 7 years. find the initial deposit. (round your answer to the nearest cent.)

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Qwline Qwline · Answer 1 · 2022-11-10T14:51:42-05:00

The initial amount of the deposit is $7234.23

Compound interest is calculated on a deposit's or a loan's initial principal as well as the accrued interest from earlier periods. Compound interest's impact is frequency-dependent. The most frequent compounding occurs with continuously compounded rewards. The mathematical maximum that compound interest can achieve is continuous compounding. Since most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.

For compound continuous problems, we use the formula [tex]A = Pe^{rt}[/tex]

where A = final amount

P = principal amount invested

e = exponent

r = rate of interest

t = time period in years

[tex]12680 = Pe^{.08(7)} \\12680 = Pe^{0.56}\\ 12680 = P*1.7506\\[/tex]

P = $7243.23

Learn more about compound interest:

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