Скачать или смотреть Future Value Formula: Interest Compounded Continuously

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Normally, we're asked to calculate compound interest either annually or monthly using the compound interest formula, y=a(1+i)^t or y=a(1+i/n)^nt, respectively...

Where:

y is the total,
a is the principal amount,
i is the interest (in decimal form),
n is the number of periods (i.e. 12 months), and
t is the number of interest periods.

If you take the limit of lim_(n→∞)⁡〖(1+1/n)^n 〗, you will end up with euler's number, e=2.71828… Therefore, instead of using that expression, we can use e instead for continuous growth: y=ae^nt

Q1. To what amount (nearest cent) will an initial deposit of $500 accumulate if invested at a compound interest rate of 6.5% per year for 8 years. Interest is computed continuously.

Q2. A quantity grows exponentially at the late of 2% per minute. By how many times will it have increased after 4 hours?