Let's say you want to compute the probability
where
converges in distribution to
, and
follows a normal distribution. The normal approximation (without the continuity correction) basically involves choosing
such that its mean and variance are the same as those for
.
Example: If
is binomially distributed with
and
, then
has mean
and variance
. So you can approximate a probability in terms of
with a probability in terms of
:
where
follows the standard normal distribution.
A = $ 861.69
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 5.5%/100 = 0.055 per year,
putting time into years for simplicity,
1 quarters ÷ 4 quarters/year = 0.25 years,
then, solving our equation
A = 850(1 + (0.055 × 0.25)) = 861.6875
A = $ 861.69
The total amount accrued, principal plus interest,
from simple interest on a principal of $ 850.00
at a rate of 5.5% per year
for 0.25 years (1 quarters) is $ 861.69.
Here is how to work 2, 3 , and 4.
It looks like they're multiplied, then you can simply add the exponents,
b⁸ * b⁴ = b⁸⁺⁴ = b¹²
remember, b⁸=b*b*b*b*b*b*b*b and b⁴=b*b*b*b
so b⁸ * b⁴ = b*b*b*b*b*b*b*b * b*b*b*b = b¹²
