SOLUTION: Suppose that $2600 is initially invested in an account with an APR of 3.3% compounded continuously.
I created this function, I don't know if it helps:
f(t)=2600e^(.033t)
And
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Question 999041: Suppose that $2600 is initially invested in an account with an APR of 3.3% compounded continuously.
I created this function, I don't know if it helps:
f(t)=2600e^(.033t)
And I calculated that the annual percent change (APY) of the account is 3.36%
What is the percent change over 10 years for this account?
Please help!
Thanks.
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose that $2600 is initially invested in an account with an APR of 3.3% compounded continuously.
I created this function, I don't know if it helps:
f(t)=2600e^(.033t)
That is correct.
-------------------------------
And I calculated that the annual percent change (APY) of the account is 3.36%
That is correct.
---------------------------
What is the percent change over 10 years for this account?
2600e^(0.033*10) = 2600*e^(0.33) = 3616.52
Percent increase in 10 years:: 1016.52/2600 = 0.391 = 39.1%
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Cheers,
Stan H.
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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the continuous compounding formula is f = p * e^rn
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
if your original investment is 2600, and your apr is 3.3% per year, and your number of years is 10, then the formula becomes:
f = 2600 * e^(.033 * 10)
the decimal equivalent of the percent is used in this calculation.
3.3% / 100 = decimal equivalent of .033.
do the math and you get f = 3616.517134.
3616.517134 / 2600 = 1.390968128
this means the future value is 1.390968128 times the original value of the investment.
this means that the future value is 139.0968128 percent of the original value.
this means that the future value is 39.0968128 percent more than the original value.
percent change is defined as shown below:
Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value.
39.0968128 appears to be representative of the percent change.
the average percent change per year would be calculated as follows:
1.390968128^(1/10) = 1.033550539 - 1 = .033550539 * 100% = 3.3550539 percent.
that rounds to 3.56% or to 3.6%, depending on how many decimal points you want to round to.
you should not, however, round intermediate results - only final results.
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