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

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

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

The solution is in the following image

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

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

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

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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