05.10.2022

A person invests 8000 dollars in a bank. The bank pays 5.25% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 12700 dollars?

. 1

Step-by-step answer

09.07.2023, solved by verified expert
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she should save it for minimum 9.1 years.

Explanation:

compound interest formula: A person invests 8000 dollars in a bank. The, №18009762, 05.10.2022 09:38where A is money earned, P is investing money, r is rate of interest, n is time.

solve:

A person invests 8000 dollars in a bank. The, №18009762, 05.10.2022 09:38

change sides

A person invests 8000 dollars in a bank. The, №18009762, 05.10.2022 09:38

take ln on both sides

A person invests 8000 dollars in a bank. The, №18009762, 05.10.2022 09:38

simplify

A person invests 8000 dollars in a bank. The, №18009762, 05.10.2022 09:38

final answer

A person invests 8000 dollars in a bank. The, №18009762, 05.10.2022 09:38

rounding to nearest tenth

A person invests 8000 dollars in a bank. The, №18009762, 05.10.2022 09:38

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Mathematics
Step-by-step answer
P Answered by Master

she should save it for minimum 9.1 years.

Explanation:

compound interest formula: \sf A = P(1+\dfrac{r}{100} )^nwhere A is money earned, P is investing money, r is rate of interest, n is time.

solve:

\hookrightarrow \sf 12700 =8000 (1+\dfrac{5.25}{100} )^n

change sides

\hookrightarrow \sf \dfrac{12700}{8000}  = (1+\dfrac{5.25}{100} )^n

take ln on both sides

\hookrightarrow \sf n\ln \left(1+\dfrac{5.25}{100}\right)=\ln \left(\dfrac{127}{80}\right)

simplify

\hookrightarrow \sf n=\frac{\ln \left(\dfrac{127}{80}\right)}{\ln \left(\dfrac{105.25}{100}\right)}

final answer

\hookrightarrow \sf n=9.03216

rounding to nearest tenth

\hookrightarrow \sf n=9.1

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
Step-by-step answer
P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

The solution is given in the image below

The solution is given in the image below
Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

Volume of rectangular prism=length * width * height

Given,

length=3/8cm

breadth=5/8cm

height=7/8cm

therefore volume=(3/8)*(5/8)*(7/8)

                           =105/512 cm3

Mathematics
Step-by-step answer
P Answered by PhD

Cost before sale tax=$46.00

Cost after including tax=$48.76

Sale tax=$48.76-46.00

=$2.76

we know,

sale tax=((sales tax rate)/100) * cost before sale tax

2.76=((sales tax rate)/100) *46.00

sale tax rate=(2.76*100)/46

                   =276/46

                    =6%

There fore sales tax rate=6%

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