# Calculus :)

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If 8000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 11 years if interest is compounded annually ____
Find the amount in the bank after 11 years if interest is compounded quaterly ____
Find the amount in the bank after 11 years if interest is compounded monthly ____
Finally, find the amount in the bank after 11 years if interest is compounded continuously

• Calculus :) -

I will do the 2nd part

i = .10/4 = .025
n = 11*4 = 44
amount = 8000(1.025)^44 = 23710.46

do #1, and #3 the same way

#4:
amount = 8000(e^(.1t))
= 8000(e^(.10*11) ) = 24033.33

• Calculus :) -

i don't understand how you set up the equation. what formula do you use for #1 & #3? please and thank you :)

• Calculus :) -

Amount = principal(1 + i)^n
where i is the periodic interest rate as a decimal
and n is the number of interest periods.

in my example, the rate was 10% , compounded quarterly, so I found
i = .10/4 = .025

and in 11 years, for quarterly compounding, there are 11*4 or 44 periods, so n = 44

in #1, i=10, n=11
amount = 8000(1.10)^11 = ...

in #3, i = .10/12 = .00833333
n = 11*12 = 132