Suppose that $1,000 is deposited in a savings account at an annual rate of 5 % . Guess the amount in the account at the end of 1 year if interest is compounded 1 quarterly, 2 monthly, 3 daily, 4 hourly. Use the compound interest formula to compute the amounts at the end of 1 year to the nearest cent. Discuss the accuracy of your initial guesses.
Suppose that $1,000 is deposited in a savings account at an annual rate of 5 % . Guess the amount in the account at the end of 1 year if interest is compounded 1 quarterly, 2 monthly, 3 daily, 4 hourly. Use the compound interest formula to compute the amounts at the end of 1 year to the nearest cent. Discuss the accuracy of your initial guesses.
Solution Summary: The author calculates the amount at the end of first year by guessing and then using the compound interest formula if interest is compounded 1000.
Suppose that
$1,000
is deposited in a savings account at an annual rate of
5
%
. Guess the amount in the account at the end of
1
year if interest is compounded
1
quarterly,
2
monthly,
3
daily,
4
hourly. Use the compound interest formula to compute the amounts at the end of
1
year to the nearest cent. Discuss the accuracy of your initial guesses.
Is it possible to show me how to come up with an exponential equation by showing all the steps work and including at least one mistake that me as a person can make. Like a calculation mistake and high light what the mistake is. Thanks so much.
iid
1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a
random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution
depend on the mean and variance of the underlying random variables (i.e., the population
mean and variance). The approximation can be written to emphasize this, using the expec-
tation and variance of one of the random variables in the sample instead of the parameters
μ, 02:
YNEY,
· (1
(EY,, varyi
n
For the following population distributions f, write the approximate distribution of the sample
mean.
(a) Exponential with rate ẞ: f(y) = ß exp{−ßy}
1
(b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ }
г(
(c) Poisson with rate λ: P(Y = y) = exp(-\}
>
y!
y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the
CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and
the standard normal CDF Fz(·).
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