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Find the future value of 575 at 5.5% compounded quarterly for 5 years. Round to the nearest cent

Readme [11.4K]

Answer:

Future value = $755.61 ( to the nearest cent)

Step-by-step explanation:

The formula for calculating the future value of an invested amount compounded periodically for a number of years is given as:

$FV = PV (1+\frac{r}{n} )^{n*t}$

where:

FV = future value = ???

PV = present value = $575

r = interest rate in decimal = 5.5% = 0.055

n = number of compounding periods per year = quarterly = 4

t = time of investment = 5 years

∴ $FV = 575 (1+\frac{0.055}{4} )^{4*5}$

$FV = 575 (1+0.01375)^{20}\\FV = 575 (1.01375 )^{20}\\FV = 575 * 1.3141\\FV = 755.607$

∴ Future value = $755.61 ( to the nearest cent)

4 0

2 years ago

What is the vertex form of the equation? y = – x^ 2 + 12 x – 4<br> show your work.

Basile [38]

11x+(-2)because you would add like terms which is -1x and 12x which is 11 then u do 2-4 which is -2

5 0

3 years ago

A manufactured lot of buggy whips has 20 items, of which 5 are defective. A random sample of 5 items is chosen to be inspected.

Finger [1]

Answer:

$P(X=1)$

And using the probability mass function we got:

$P(X=1) = (5C1) (0.25)^1 (1-0.25)^{5-1}= 0.396$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

For this cae that one buggy whip would be defective is $p = \frac{5}{20}=0.25$

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=5, p=0.25)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X=1)$

And using the probability mass function we got:

$P(X=1) = (5C1) (0.25)^1 (1-0.25)^{5-1}= 0.396$

3 0

3 years ago

A brand new video game system sells for $340. If the sales tax is 6.98%, how much will the new video game

tiny-mole [99]

$363.73
The sales tax is $23.73

Steps:
Sales tax is calculated by multiplying the purchase price by the sales tax rate to get the amount of sales tax due. The sales tax added to the original purchase price produces the total cost of the purchase.

So 340 • 6.89%
340• .0698= 23.732
If it’s a percentage you move the decimal two places to the left
340 + 23.73 = 363.73

Hope this helps

6 0

3 years ago

What is the answer to 10 less than 38 is

Alex

28 because you do 38-10 which equals 28. Hope I helped.

4 0

3 years ago

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