If $100 is deposited in a savings account that earns interest at an annual rate of 4 1/2% compounded continuously, what is the value of the account at the end of two years?

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Answer 1 · 2018-06-08T06:37:31

Jun 8, 2018

See alan_n

Answer 2 · 2018-06-09T06:57:33

#$109.42#

The formula for compound interest calculation where the compounding occurs continuously is:

#A_t = Pe^(rt)#

Where:

#A_t# is the amount after #t# years
#P# is the principal amount
#r# is the annual interest rate
#e# is Euler's number #approx 2.71828#

In this example: #P=$100, r=4.5% = 0.045#

#:. P_2 =100xx e^(0.045xx2)#

#approx 100 xx 2.71828^0.09#

#=$109.42# To 2D

NB: For those interested in the derivation of the formula it stems from the limit definition of #e#. Also see: http://www.milefoot.com/math/calculus/limits/LimitDefinitionOfE10.htm