11.05.2021

Paisley is going to invest in an account paying an interest rate of 3.4% compounded daily. how much would paisley need to invest, to the nearest dollar, for the value of the account to reach $400 in 16 years?

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Mathematics

Paisley is going to invest in an account paying an interest rate of 3.4% compounded daily. How much would Paisley need to invest, to the nearest dollar, for the value of the account to reach $400 in 16 years?

Step-by-step answer

P Answered by Specialist

232

Step-by-step explanation:

Paisley is going to invest in an account paying an interest rate of 3.4% compounded

daily. How much

Mathematics

Paisley invested $3,000 in an account paying an interest rate of 3% compounded continuously. Maya invested $3,000 in an account paying an interest rate of 4% compounded daily. To the nearest hundredth of a year, how much longer would it take for Paisley s money to triple than for Maya s money to triple?

Step-by-step answer

P Answered by PhD

9.15 years

Step-by-step explanation:

step 1

Paisley

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=?\ years\\ P=\$3,000\\ r=0.03\\A=\$9,000$

substitute in the formula above

$9,000=3,000(e)^{0.03t}$

solve for t

$3=(e)^{0.03t}$

apply ln both sides

$ln(3)=ln(e)^{0.03t}$

ln(3)=(0.03t)ln(e)

ln(3)=(0.03t)

solve for t

t=ln(3)/(0.03)

$t=36.62\ years$

step 2

Maya

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=?\ years\\ P=\$3,000\\ r=0.04\\A=\$9,000\\n=365$

substitute in the formula above

$9,000=3,000(1+\frac{0.04}{365})^{365t}$

solve for t

$3=(\frac{365.04}{365})^{365t}$

Apply log both sides

$log(3)=log(\frac{365.04}{365})^{365t}$

$log(3)=(365t)log(\frac{365.04}{365})$

$t=log(3)/[(365)log(\frac{365.04}{365})]$

$t=27.47\ years$

step 3

we know that

To find out how much longer would it take for Paisley's money to triple than for Maya's money to triple find the difference in years

$36.62-27.47=9.15\ years$

Mathematics

Step-by-step answer

P Answered by PhD

9.15 years

Step-by-step explanation:

step 1

Paisley

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=?\ years\\ P=\$3,000\\ r=0.03\\A=\$9,000$

substitute in the formula above

$9,000=3,000(e)^{0.03t}$

solve for t

$3=(e)^{0.03t}$

apply ln both sides

$ln(3)=ln(e)^{0.03t}$

ln(3)=(0.03t)ln(e)

ln(3)=(0.03t)

solve for t

t=ln(3)/(0.03)

$t=36.62\ years$

step 2

Maya

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=?\ years\\ P=\$3,000\\ r=0.04\\A=\$9,000\\n=365$

substitute in the formula above

$9,000=3,000(1+\frac{0.04}{365})^{365t}$

solve for t

$3=(\frac{365.04}{365})^{365t}$

Apply log both sides

$log(3)=log(\frac{365.04}{365})^{365t}$

$log(3)=(365t)log(\frac{365.04}{365})$

$t=log(3)/[(365)log(\frac{365.04}{365})]$

$t=27.47\ years$

step 3

we know that

To find out how much longer would it take for Paisley's money to triple than for Maya's money to triple find the difference in years

$36.62-27.47=9.15\ years$

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

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

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

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

A new school randomly assigns a six-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?

Step-by-step answer

P Answered by PhD

The total nom of code that can be used is equal to 5+3 = 8

Mathematics

In a parking lot, for every 8 cars there are 7 trucks. What is the ratio of cars to trucks? A)7 : 8 B)8 : 7 C)8 : 15 D)15 : 8

Step-by-step answer

P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics

The ratio of tables to chairs at the furniture store is 1:6. There are 30 chairs. How many tables are there?

Step-by-step answer

P Answered by PhD

The solution is in the following image

Mathematics

The value of a collectible coin can be represented by the equation y = 2 x + 15, where x represents its age in years and y represents its total value in dollars. What is the value of the coin after 19 years? $2 $23 $38 $53

Step-by-step answer

P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics

the surface area of a box is 232 square inches. the box is 4 inches wide and 8 inches long. what is the hight?

Step-by-step answer

P Answered by PhD

The solution is given in the image below

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Paisley is going to invest in an account paying an interest rate of 3.4% compounded daily. how much would paisley need to invest, to the nearest dollar, for the value of the account to reach $400 in 16 years? ​

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Paisley is going to invest in an account paying an interest rate of 3.4% compounded daily. how much would paisley need to invest, to the nearest dollar, for the value of the account to reach $400 in 16 years?