Please help!!!
1 answer:
Answer:
Step-by-step explanation:
<u>Compound Interest</u>
It's the type of financial calculations that includes the interest of previous periods into the new interests earned by some initial investment or principal P.
If we want to compute the final value FV of a series of n payments R at a fixed compound interest rate i, then
Where
The question provides us the following data
i=10% compounded twice a year
n=3 1/2 years
FV=15,000
We need to convert the number of periods and the interest rate to a semester base:
Let's calculate Fm
Knowing that
Solving for R
Sara should deposit $1,842.30 twice a year to have the down payment for her own restaurant
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Answer:
(a) $1,020 or more = 0.2358
(b) Between $880 and $1,130 = 0.7389
(c) Between $830 and $940 = 0.3524
(d) Less than $770 = 0.0294
Step-by-step explanation:
We are given that According to M/PF Research, Inc. report, the average cost of renting an apartment in Minneapolis is $951.
Suppose that the standard deviation of the cost of renting an apartment in Minneapolis is $96 and that apartment rents in Minneapolis are normally distributed.
<em>Let X = apartment rents in Minneapolis</em>
So, X ~ Normal()
The z score probability distribution for normal distribution is given by;
<em> </em> Z = ~ N(0,1)
where, = average cost of renting an apartment = $951
= standard deviation = $96
(a) Probability that the price is $1,020 or more is given by = P(X $1,020)
P(X $1,020) = P(
) = P(Z
0.72) = 1 - P(Z < 0.72)
= 1 - 0.76424 = 0.2358
<em>The above probability is calculated by looking at the value of x = 0.72 in the z table which gives an area of 0.76424.</em>
<em />
(b) Probability that the price is between $880 and $1,130 is given by = P($880 < X < $1,130) = P(X < $1,130) - P(X 880)
P(X < $1,130) = P( <
) = P(Z < 1.86) = 0.96856
P(X $880) = P(
) = P(Z
-0.74) = 1 - P(Z < 0.74)
= 1 - 0.77035 = 0.22965
<em>The above probability is calculated by looking at the value of x = 1.86 and x = 0.74 in the z table which gives an area of 0.96856 and 0.77035 respectively.</em>
<em />
Therefore, P($880 < X < $1,130) = 0.96856 - 0.22965 = 0.7389
<em />
(c) Probability that the price is between $830 and $940 is given by = P($830 < X < $940) = P(X < $940) - P(X 830)
P(X < $940) = P( <
) = P(Z < -0.11) = 1 - P(Z
0.11)
= 1 - 0.5438 = 0.4562
P(X $830) = P(
) = P(Z
-1.26) = 1 - P(Z < 1.26)
= 1 - 0.89617 = 0.10383
<em>The above probability is calculated by looking at the value of x = 0.11 and x = 1.26 in the z table which gives an area of 0.5438 and 0.89617 respectively.</em>
<em />
Therefore, P($830 < X < $940) = 0.4562 - 0.10383 = 0.3524
(d) Probability that the price is Less than $770 is given by = P(X < $770)
P(X < $770) = P( <
) = P(Z < -1.89) = 1 - P(Z
1.89)
= 1 - 0.97062 = 0.0294
<em>The above probability is calculated by looking at the value of x = 1.89 in the z table which gives an area of 0.97062.</em>