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statuscvo [17]
3 years ago
15

Ted invests $8,310 in a savings account with a fixed annual interest rate of 2% compounded continuously. How long will it take f

or the account balance to reach it take for the account balance to reach $9,751.88?
Mathematics
1 answer:
Vsevolod [243]3 years ago
8 0

Answer: It will take 8 years.

Step-by-step explanation:

Equation for interest compounded continuously:

A=Pe^{rt} , A = accumulated amount , P=Principal value , r =rate of interest , t= time.

Given: P=  $8,310 , r = 2%  , A= $9,751.88

9751.88=8310e^{0.02t}\\\\\Rightarrow\ \dfrac{9751.88}{8310}=e^{0.02t}\\\\\Rightarrow\ 1.17351143201=e^{0.02t}

Taking natural log on both sides

\ln (1.17351143201)=\ln (e^{0.02t})\\\\\Rightarrow\ 0.160000478068=0.02t\\\\\Rightarrow\ t=\dfrac{0.160000478068}{0.02}\\\\\Rightarrow\ t=8.0000239034\approx8

Hence, it will take 8 years.

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App 19.study
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Answer:

1 \to 22 \to 0.176

2 \to 13 \to 0.104

3 \to 18 \to 0.144

4 \to 29 \to 0.232

5 \to 37 \to 0.296

6 \to 6 \to 0.048

Step-by-step explanation:

Given

n = 125

See attachment for proper table

Required

Complete the table

Experimental probability is calculated as:

Pr = \frac{Frequency}{n}

We use the above formula when the frequency is known.

For result of roll 2, 4 and 6

The frequencies are 13, 29 and 6, respectively

So, we have:

Pr(2) = \frac{13}{125} = 0.104

Pr(4) = \frac{29}{125} = 0.232

Pr(6) = \frac{6}{125} = 0.048

When the frequency is to be calculated, we use:

Pr = \frac{Frequency}{n}

Frequency = n * Pr

For result of roll 3 and 5

The probabilities are 0.144 and 0.296, respectively

So, we have:

Frequency(3) = 125 * 0.144 = 18

Frequency(5) = 125 * 0.296 = 37

For roll of 1 where the frequency and the probability are not known, we use:

Total \ Frequency = 125

So:

Frequency(1) added to others must equal 125

This gives:

Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125

Frequency(1) + 103 = 125

Collect like terms

Frequency(1) =- 103 + 125

Frequency(1) =22

The probability is then calculated as:

Pr(1) = \frac{22}{125}

Pr(1) = 0.176

So, the complete table is:

1 \to 22 \to 0.176

2 \to 13 \to 0.104

3 \to 18 \to 0.144

4 \to 29 \to 0.232

5 \to 37 \to 0.296

6 \to 6 \to 0.048

5 0
3 years ago
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