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You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate

DanielleElmas [232]

It takes 10.155 years until you have $3,000 ⇒ 3rd

Step-by-step explanation:

The formula for compound interest, including principal sum is:

$A=P(1+\frac{r}{n})^{nt}$ , where

A is the future value of the investment/loan, including interest
P is the principal investment amount
r is the annual interest rate (decimal)
n is the number of times that interest is compounded per unit t
t is the time the money is invested or borrowed for

∵ You decide to put $2,000 in a savings account

∴ P = 2000

∵ You want to save for $3,000

∴ A = 3000

∵ The account has an interest rate of 4% per year and is

compounded monthly

∴ r = 4% = 4 ÷ 100 = 0.04

∴ n = 12 ⇒ compounded monthly

- Substitute all of these values in the formula above to find t

∵ $3000=2000(1+\frac{0.04}{12})^{12t}$

- Divide both sides by 2000

∴ $1.5=(1+\frac{1}{300})^{12t}$

∴ $1.5=(1\frac{1}{300})^{12t}$

- Change the mixed number to an improper fraction

∴ $(1.5)=(\frac{301}{300})^{12t}$

- Insert ㏒ for both sides

∴ $log(1.5)=log(\frac{301}{300})^{12t}$

- Remember $log(a)^{n}=nlog(a)$

∴ $log(1.5)=(12t)log(\frac{301}{300})$

- Divide both sides by $log(\frac{301}{300})$

∴ 121.84 = 12 t

- Divide both sides by 12

∴ 10.155 = t

It takes 10.155 years until you have $3,000

Learn more:

You can learn more about the compound interest in brainly.com/question/4361464

#LearnwithBrainly

5 0

3 years ago

Maths help please!!!!!! PART B ONLY

andreyandreev [35.5K]

Answer:

19.37.

Step-by-step explanation:

Integrating the function we get

x^4/4 - 5x^3/3 + x^2 + 8x

Area under the curve from x = -1 to x = 0

= (-1)^4/4 - 5(-1)^3/3 + (-1)^2 - 8

= 5.083

In a similar way we calculate area from 0 to 2

this = 10.667.

Total = 15.75.

Now we subtract 12.13 to get the area from x = 2 to x =p.

= 15.75 - 12.13 = 3.62

So total shaded area = 15.75 + 3.62

= 19.37.

5 0

2 years ago

Harry's motorboat can make an average of 8 miles per hour. one day he sets out for a trip, only to have the motor break down. ha

melisa1 [442]

He rowed 10 miles in total. YOU'RE WELCOME :D

5 0

3 years ago

What is 10r-5r+3r-8r?????

ANEK [815]

Answer:

16

Step-by-step explanation:

8 0

3 years ago

Suppose the number of births that occur in a hospital can be assumed to have a Poisson distribution with parameter = the average

arsen [322]

Answer:

0.5372

Step-by-step explanation:

Given that the number of births that occur in a hospital can be assumed to have a Poisson distribution with parameter = the average birth rate of 1.8 births per hour.

Let X be the no of births in the hospital per hour

X is Poisson

with mean = 1.8

the probability of observing at least two births in a given hour at the hospital

= $P(X\geq 2)\\= 1-F(1)\\= 1-0.4628\\= 0.5372$

the probability of observing at least two births in a given hour at the hospital = 0.5372

4 0

3 years ago