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rodikova [14]
3 years ago
9

You need $20,000 to make a down payment on a house. Your beginning balance in your checking account this month was $5,678. Your

ending balance was $6,324. Assuming your account balance continues to grow at the same rate, how long until you have enough money to make the down payment?
Mathematics
1 answer:
Kamila [148]3 years ago
6 0

22.1649 months

Step-by-step explanation:

We begin by calculating the interest accruing to the principal amount in the bank account;

$6,324 - $5,678

= $646

646/5678 * 100

= 11.38 % pm

Now that know the interest rate, we calculate the amount of time it will take to accrue to $20,000

A = P(1 + rt)

Where:

   A = Total Accrued Amount (principal + interest)

   P = Principal Amount

   r = Rate of Interest per year in decimal; r = R/100

   t = Time Period involved in months or years

20000 = 5678 (1 + 0.1138t)

20000 = 5678 + 646.1564t

20000 – 5678 = 646.1564t

14,322 = 646.1564t

t = 14,322/646.1564

t = 22.1649

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7(x+2)=7x-10 perform indicated multiplication on the left side

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6 0
3 years ago
Find the amount that is in the account if $4500 is compounded daily at 3.25% for 6 years
Sindrei [870]

Step-by-step explanation:

1st year interest calculated = 3.25/100 × $4500/1 = $146.25

2nd year principal = 1st year principal + 1st year interest = $4500 + $146.25 = $4646.25. 2nd year interest calculated = 3.25/100 ×$4646.25/1 =$151

3rd year principal = 2nd principal + 2nd year interest = $4646.25 + $151 = $4797.25. 3rd year interest calculated = 3.25/100 × $4797.25/1 = $155.91

4th year principal = 3rd year principal + 3rd year interest =$4797.25 + $155.91 =$4953.16. 4th year principal calculated = 3.25/100 × 4953.16/1 =$160.98

5th year principal = 4th year principal + 4 year interest = &4953.16 +$160.98 = $5114.14. 5th year interest calculated = 3.25/100 × 5114.14/1 =$166.21

6th year principal =5th year principal + 5th year interest = $5114.14 + $166.21 =$5280.35. 6th year interest calculated = 3.25/100 × 5280.35/1 =$171.61

Amount = main principal + compound interest =$4500 +&146.25 +$151+$155.91+$160.98+$166.21+$171.61 =$5451.96

6 0
3 years ago
The number of internet users in mexico between 2004 and 2008 can be modeled as u(t) = 8.02(1.17t) million users where t is the n
maxonik [38]

Answer:

a) 1.479 Million

b) 36.9%

c) 13.668%

Step-by-step explanation:

The complete question is attached in the image below.

The number of internet users in Mexico between 2004 and 2008 is modelled by the following equation:

u(t)=8.02(1.17)^{t}

Where, u(t) is in millions and t is the number of years since 2004.

Part a) Rate of change of internet users between 2004 and 2006

The rate of change of a function is defined as:

\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}

We have to find the rate of change between 2004 and 2006. For 2004 t = 0, and for 2006, t = 2. So the rate of change for the given function will be:

\frac{u(2)-u(0)}{2-0}\\\\ =\frac{8.02(1.17)^{2}-8.02(1.17)^{0}}{2}\\\\ =1.479

Thus, the average rate of change in number of internet users in Mexico from between 2004 and 2006 was 1.479 million.

Part b) Percentage change of internet users between 2004 and 2006

The formula to calculate the percentage change is:

\frac{\text{New value - Original Value}}{\text{Original Value}} \times 100\%

Here, New value means the users in 2006 and original value means the users in 2004.

Using the values in this formula, we get:

\frac{8.02(1.17)^{2}-8.02(1.17)^0}{8.02(1.17)^{0}} \times 100\%\\\\  =36.89\%

Thus, the percentage change in the number of internet users between 2004 and 2006 was 36.89%

Part c) Percentage of internet users in 2008

For 2008, t would be equal to 4.

So, the number of internet users in Mexico in 2008 would be = 8.02(1.17)^{4}=15.02857542 million = 15,028,575 (rounded to nearest integer)

Total population of Mexico in 2008 = 109,955,400

We have to calculate what percentage of Mexico population was Internet users in 2008. The formula for this would be:

\frac{\text{Concerned Value}}{\text{Total Value}} \times 100\%

Here, concerned value is the number of internet users and total value is the total population. Using the values in this formula we get:

\frac{15028575}{109955400} \times 100\%\\\\=13.668\%

Thus, 13.668% of the population was internet users in 2008 in Mexico.

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