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kvv77 [185]
3 years ago
15

$765.13 is deposited at the end of each month for 3 years in an account paying 2% Interest compounded monthly. Find the final am

ount of the account. Round to the nearest
cent
O A. $27,598.32
OB. $28,363,45
OC. $29,128.58
OD. $26,787.27
Mathematics
1 answer:
Crank3 years ago
8 0

Answer:

Option B.

Step-by-step explanation:

The future value formula, for an annuity, is:

FV = \frac{P((1+r)^{n} - 1)}{r}

An annuity means that a number of payments happen during the period(an year, for example).

P is the value of the deposit, r is the interest rate, as a decimal, and n is the number of deposits.

In this question:

Deposits of $765.13, so P = 765.13

Each month, for 3 years. An year has twelve months, so n = 3*12 = 36

2% Interest a year. An year has 12 months, so r = \frac{0.02}{12} = 0.00167

Find the final amount of the account.

FV = \frac{765.13*((1 + 0.00167)^{36} - 1)}{0.00167} = 28,363.46

The final amount of the account will be $28,363.46, which is option B.

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Mark buys a used car for $12,000. The value of the car depreciates 10% per year from the time he bought the car.
timama [110]

Answer:

option D

Step-by-step explanation:

r = 10% = 0.10

v(t) = P (1 - r)^t\\\\V(t) = 12000(1 - 0.10)^t\\\\V(t) = 12000\times (0.9)^t

4 0
3 years ago
Tessa bought stock in a restaurant for $173.00. Her stock is now worth $242.20. What is the percentage increase of the value of
frozen [14]

Answer:

The percentage increase in Tessa's stock is 40%

Step-by-step explanation:

Given that:

Previous worth = $173

Worth now = $242.20

We have to find percentage increase which can be known by subtracting previous worth from present worth and multiplying it by 100:

Percentage increase = $242.20 - $173 = $69.2

Percentage increase = $69.2/173 *100

Percentage increase = 40%

i hope it will help you!

7 0
3 years ago
John, Joe, and James go fishing. At the end of the day, John comes to collect his third of the fish. However, there is one too m
Dmitry [639]

Answer:

The minimum possible initial amount of fish:52

Step-by-step explanation:

Let's start by saying that

x = is the initial number of fishes

John:

When John arrives:

  • he throws away one fish from the bunch

x-1

  • divides the remaining fish into three.

\dfrac{x-1}{3} + \dfrac{x-1}{3} + \dfrac{x-1}{3}

  • takes a third for himself.

\dfrac{x-1}{3} + \dfrac{x-1}{3}

the remaining fish are expressed by the above expression. Let's call it John

\text{John}=\dfrac{x-1}{3} + \dfrac{x-1}{3}

and simplify it!

\text{John}=\dfrac{2x}{3} - \dfrac{2}{3}

When Joe arrives:

  • he throws away one fish from the remaining bunch

\text{John} -1

  • divides the remaining fish into three

\dfrac{\text{John} -1}{3} + \dfrac{\text{John} -1}{3} + \dfrac{\text{John} -1}{3}

  • takes a third for himself.

\dfrac{\text{John} -1}{3}+ \dfrac{\text{John} -1}{3}

the remaining fish are expressed by the above expression. Let's call it Joe

\text{Joe}=\dfrac{\text{John} -1}{3}+ \dfrac{\text{John} -1}{3}

and simiplify it

\text{Joe}=\dfrac{2}{3}(\text{John}-1)

since we've already expressed John in terms of x, we express the above expression in terms of x as well.

\text{Joe}=\dfrac{2}{3}\left(\dfrac{2x}{3} - \dfrac{2}{3}-1\right)

\text{Joe}=\dfrac{4x}{9} - \dfrac{10}{9}

When James arrives:

We're gonna do this one quickly, since its the same process all over again

\text{James}=\dfrac{\text{Joe} -1}{3}+ \dfrac{\text{Joe} -1}{3}

\text{James}=\dfrac{2}{3}\left(\dfrac{4x}{9} - \dfrac{10}{9}-1\right)

\text{James}=\dfrac{8x}{27} - \dfrac{38}{27}

This is the last remaining pile of fish.

We know that no fish was divided, so the remaining number cannot be a decimal number. <u>We also know that this last pile was a multiple of 3 before a third was taken away by James</u>.

Whatever the last remaining pile was (let's say n), a third is taken away by James. the remaining bunch would be \frac{n}{3}+\frac{n}{3}

hence we've expressed the last pile in terms of n as well.  Since the above 'James' equation and this 'n' equation represent the same thing, we can equate them:

\dfrac{n}{3}+\dfrac{n}{3}=\dfrac{8x}{27} - \dfrac{38}{27}

\dfrac{2n}{3}=\dfrac{8x}{27} - \dfrac{38}{27}

L.H.S must be a Whole Number value and this can be found through trial and error. (Just check at which value of n does 2n/3 give a non-decimal value) (We've also established from before that n is a multiple a of 3, so only use values that are in the table of 3, e.g 3,6,9,12,..

at n = 21, we'll see that 2n/3 is a whole number = 14. (and since this is the value of n to give a whole number answer of 2n/3 we can safely say this is the least possible amount remaining in the pile)

14=\dfrac{8x}{27} - \dfrac{38}{27}

by solving this equation we'll have the value of x, which as we established at the start is the number of initial amount of fish!

14=\dfrac{8x}{27} - \dfrac{38}{27}

x=52

This is minimum possible amount of fish before John threw out the first fish

8 0
2 years ago
It takes a ant farm 3 days to comsume 1/2 of an apple.At that rate,in how many days will the ant farm consume 3 apples?
alexgriva [62]

Answer:

18

Step-by-step explanation:

In three days, the ant farm consumed 1/2 an apple. In 6 days the ant farm will consume 1 apple. We can multiply 6 days by 3 for three apples.

6(3)=18 days

5 0
2 years ago
Can someone please help me./ solve.
Zina [86]

Answer:f=99

Step-by-step explanation

solve for f by simplifying both sides of the equation, then isolating the variable.

7 0
2 years ago
Read 2 more answers
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