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If a payment $P is made every year into an account that attracts a fixed interest rate...

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nerdygirl-1996 | Student, Undergraduate | Honors

Posted May 27, 2013 at 12:16 PM via web

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If a payment $P is made every year into an account that attracts a fixed interest rate of r % per annum compounded continuously pans the account is closed t years later the balance due will be: 

`(P(e^0.01rt-1)/(1-e^-0.01r)` )

where e is eulers number 

a.) find the balance due after 10 years if 2000 dollars is invested each year and the interest rate is fixed at 10% per annum compounded continuously 

b. ) find the number if years the scheme must run if an investor wants to invest  3000 dollars per year and close the account whenthe balance reaches 154000 dollars, assuming a constant interest rate of 8 percent per year compounded continuosly 

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pramodpandey | College Teacher | Valedictorian

Posted May 27, 2013 at 1:34 PM (Answer #1)

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I am assuming your expression is
`A=(p(e^(.01rt)-1))/(1-e^(-.01r))`

If it is incorrect,we will have to work out,  

$2000 is invested each year, so P = 2000.
r is the interest rate, which is given as 10%. Thus, r = 10
We need to find the balance due after 10 years, so t = 10.

Hence, the balance due will be
Balance A=`(2000(e^(.01xx10xx10)-1))/(1-e^(-.01xx10))`
`=(2000xx1.7182818)/(0.09510)`
`=36135.19$`

b.
$3000 is invested each year, so P = 3000.
r is the interest rate, which is given as 8%. Thus, r = 8
We need to find the balance =15400
 due after years, so t = ?.

`15400=(3000(e^(.01xx8xxt)-1))/(1-e^(-.01xx8))`
`(15400xx.0768836)/3000=e^(.08t)-1`
`.394669+1=e^.08t`
`1.394669=e^(.08t)`
`.08t=ln(1.394669)`
`.08t=.332657111`
`t=4.158` (approx)
approximately
t=4 years.

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