Suppose you make a deposit of $P into a savings account that earns interest at a rate

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Suppose you make a deposit of $P into a savings account that earns interest at a rate of 100 r% per year. 

a. Show that if interest is compounded once per year, then the balance after t years is B(t) = P(1 + r)t.

b. If interest is compounded m times per year, then the balance after t years is B(t) = P(1 + r/m)mt. For example, m = 12 corresponds to monthly compounding, and the interest rate for each month is r/12. In the limit m→∞, the compounding is said to be continuous. Show that with continuous compounding, the balance after t years is B(t) = Pert.

Compounding
Compounding is the process in which an asset's earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will...
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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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