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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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

Mark D.

Jun 8, 2018

See alan_n

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Answer 2 · 2018-06-09T06:57:33

$$ 109.42$ $$109.42$

Explanation:

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

$A_{t} = P e^{r t}$ $A_t = Pe^(rt)$

Where:

$A_{t}$ $A_t$ is the amount after $t$ $t$ years
$P$ $P$ is the principal amount
$r$ $r$ is the annual interest rate
$e$ $e$ is Euler's number $\approx 2.71828$ $approx 2.71828$

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

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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?

2 Answers

Explanation:

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