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mixer [17]
3 years ago
15

Diego decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded

quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account?
Mathematics
2 answers:
Ivenika [448]3 years ago
7 0

Answer: it will take 17.5 years to double his money in the account.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $500

A = 500 × 2 = $1000

r = 4% = 4/100 = 0.04

n = 4 because it was compounded 3 times in a year.

Therefore,.

1000 = 500(1 + 0.04/4)^4 × t

1000/500 = (1 + 0.01)^4t

2 = (1.01)^4t

Taking log of both sides, it becomes

Log2 = 4tlog 1.01

0.301 = 4t × 0.0043 = 0.0172t

t = 0.301/0.0172

t = 17.5 years

kykrilka [37]3 years ago
3 0

Answer: it will take 17.5 years to double his money in the account.

Step-by-step explanation:

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3 years ago
A company establishes a fund of 120 from which it wants to pay an amount,C, to any of its 20 employees who achieve a high-perfor
Leno4ka [110]

Answer:

C=120/2=60

Step by step Explanation'

To solve this problem, we will need to apply trial-and-error calculation with the binomial distribution, even though it appears like Central Limit Theorem but it's not.

For us to know the value of C , we will look for a minimum integer such that having 'n' number of high performance level of employee has the probability below 0.01.

Determine the maximum value of C, then the maximum value that C can have is 120/n

Let us represent X as the number of employees with high performance with a binomial distribution of

P =0.02( since the percentage of chance of achieving a high performance level is 2%)

n = 20 ( number of employees who achieve a high performance level)

The probability of X= 0 can be calculated

P( X= 0) = 0.98^n

P(X=0)=0.98^20

P(X=0)=0.668

P(X=1)=0.02*20*0.98^19

P(X=1)=0.272

P(X=2)=0.02^2*20*0.98^18

P(X=2)=0.053

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BUT the summation of P( X= 0)+ P( X= 1) will give the value of 0.94 which doesn't exceed the 0.99 value,

Therefore, the minimum value of integer in such a way that P(X >2) is less than 0.01 have n= 2

then the maximum value that C can have is 120/n

C=120/2=60

7 0
4 years ago
Material for a dress costs £5.50 per metre.<br> find the cost of 10cm and 70cm
Zielflug [23.3K]

Answer:

<em>The cost of 10 cm and 70 cm are  £0.55 and £3.85 respectively.</em>

Step-by-step explanation:

Material for a dress costs £5.50 per meter.

We know that,  <u>1 meter = 100 cm</u>.

Suppose, the cost of 10 cm material is x and the cost of 70 cm material is y

Now, <u>according to the ratio of "cost" to the "length of material"</u> , we will get.......

\frac{x}{10} =\frac{5.50}{100}\\ \\ 100x=10*5.50=55\\ \\ x=\frac{55}{100}=0.55

and

\frac{y}{70} =\frac{5.50}{100}\\ \\ 100y=70*5.50=385\\ \\ x=\frac{385}{100}=3.85

So, the cost of 10 cm material is £0.55 and the cost of 70 cm material is £3.85

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