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11.07.2021

How much money will be in Account A at the end of 3 years? $ How much money will be in Account B at the end of 3 years? $.

Step-by-step answer

09.07.2023, solved by verified expert

Rajat Thapa

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Mathematics, DAV Post Graduate College

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Account A is having $1,093 after 3 years. and Account B is having $1,120 after 3 years.

What is compound interest?

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

Elisa put $1,000 in each bank.

Account A: gives her at a rate of 3% per annum compounded annually.

Account B: $40 bonus is added to the account each year.

After 3 years, account A will have

Account A is having $1,093 after 3 years.

After 3 years, account B will have

Account B is having $1,120 after 3 years.

More about the compound interest link is given below.

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Mathematics

How much money will be in Account A at the end of 3 years? $ How much money will be in Account B at the end of 3 years? $.

Step-by-step answer

P Answered by Specialist

Account A is having $1,093 after 3 years. and Account B is having $1,120 after 3 years.

What is compound interest?

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

Elisa put $1,000 in each bank.

Account A: gives her at a rate of 3% per annum compounded annually.

Account B: $40 bonus is added to the account each year.

After 3 years, account A will have

$\rm Account \ A = 1000(1.03)^3\\\\Account \ A = 1093$

Account A is having $1,093 after 3 years.

After 3 years, account B will have

$\rm Account \ B= 1000 + 3(40)\\\\Account \ B= 1,120$

Account B is having $1,120 after 3 years.

More about the compound interest link is given below.

Mathematics

you deposit $3000 into a money-market savings account which pays 4.8% compounded quarterly, and you make no withdrawals from or further deposits into this account for 3 years. how much money is in your account at the end of those 3 years? give answer in dollars rounded to the nearest cent. do not enter $ sign in answer.

Step-by-step answer

P Answered by PhD

$5265.71

Step-by-step explanation:

We have been given that you deposit $3000 into a money-market savings account which pays 4.8% compounded quarterly.

We will use future value formula to solve our given problem.

$FV=C_0\times (1+r)^n$ , where,

$C_0=\text{Initial amount}$ ,

r = Rate of return in decimal form,

n = Number of periods.

$4.8\%=\frac{4.8}{100}=0.048$

$n=3\times 4=12$

$FV=\$3,000\times (1+0.048)^{12}$

$FV=\$3,000\times (1.048)^{12}$

$FV=\$3,000\times 1.7552354909370114$

$FV=\$5265.7064\approx \$5265.71$

Therefore, there will be $5265.71 in your account at the end of those 3 years.

Mathematics

Step-by-step answer

P Answered by PhD

$5265.71

Step-by-step explanation:

We have been given that you deposit $3000 into a money-market savings account which pays 4.8% compounded quarterly.

We will use future value formula to solve our given problem.

$FV=C_0\times (1+r)^n$ , where,

$C_0=\text{Initial amount}$ ,

r = Rate of return in decimal form,

n = Number of periods.

$4.8\%=\frac{4.8}{100}=0.048$

$n=3\times 4=12$

$FV=\$3,000\times (1+0.048)^{12}$

$FV=\$3,000\times (1.048)^{12}$

$FV=\$3,000\times 1.7552354909370114$

$FV=\$5265.7064\approx \$5265.71$

Therefore, there will be $5265.71 in your account at the end of those 3 years.

Mathematics

Mary seitz invested a certain amount of money in a savings account paying 5% simple interest per year. when she withdrew her money at the end of 3 years, she received $300 in interest. how much money did mary place in the savings account? mary seitz invested $ blank in the savings account.

Step-by-step answer

P Answered by PhD

Mary Seitz invested $ 2,000 in the savings account.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Interest rate = 5% simple = 0.05

Time of the investment = 3 years

Amount of interest = $ 300

2. How much money did Mary place in the savings account?

Let's recall the formula of the simple interest:

A = P * (1 + rt), where:

A = Final value of the investment

P = Initial investment

r = Interest rate

t = Time

Replacing with the values we know:

A = P * (1 + 0.05 * 3)

A = P * (1 + 0.15)

P + 300 = 1.15P (A = P + 300)

P - 1.15P = -300

-0.15P = -300

P = -300/-0.15

P = 2,000

Mary Seitz invested $ 2,000 in the savings account.

Mathematics

Step-by-step answer

P Answered by PhD

Mary Seitz invested $ 2,000 in the savings account.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Interest rate = 5% simple = 0.05

Time of the investment = 3 years

Amount of interest = $ 300

2. How much money did Mary place in the savings account?

Let's recall the formula of the simple interest:

A = P * (1 + rt), where:

A = Final value of the investment

P = Initial investment

r = Interest rate

t = Time

Replacing with the values we know:

A = P * (1 + 0.05 * 3)

A = P * (1 + 0.15)

P + 300 = 1.15P (A = P + 300)

P - 1.15P = -300

-0.15P = -300

P = -300/-0.15

P = 2,000

Mary Seitz invested $ 2,000 in the savings account.

Mathematics

Mary seitz invested a certain amount of money in a savings account paying 4% simple interest per year. when she withdrew her money at the end of 3 years, she received $ 480 in interest. how much money did mary place in the savings account?

Step-by-step answer

P Answered by PhD

Answer

Find out the how much money did Mary place in the savings account .

To prove

Formula

$Simple\ interest = \frac{Principle\times rate\times time}{100}$

As given

Mary Seitz invested a certain amount of money in a savings account paying 4% simple interest per year.

When she withdrew her money at the end of 3 years, she received $ 480 in interest.

Interest = $480

Time = 3 years

Rate = 4%

Put in the formula

$480 = \frac{Principle\times 4\times 3}{100}$

$Principle = \frac{48000}{12}$

Principle = $ 4000

Therefore the $4000 money Mary place in the saving account.

Mathematics

Step-by-step answer

P Answered by PhD

Answer

Find out the how much money did Mary place in the savings account .

To prove

Formula

$Simple\ interest = \frac{Principle\times rate\times time}{100}$

As given

Mary Seitz invested a certain amount of money in a savings account paying 4% simple interest per year.

When she withdrew her money at the end of 3 years, she received $ 480 in interest.

Interest = $480

Time = 3 years

Rate = 4%

Put in the formula

$480 = \frac{Principle\times 4\times 3}{100}$

$Principle = \frac{48000}{12}$

Principle = $ 4000

Therefore the $4000 money Mary place in the saving account.

Mathematics

Julien s parents want $64,000 at the end of 3 years. They put their money in an account that yields 10% per year compounded monthly. Julien s parents should deposit $. Round your answer to the nearest dollar.

Step-by-step answer

P Answered by Specialist

$\$47,471$

Step-by-step explanation:

Given

Julien's parents want $64,000 at the end of 3 years

The rate of interest is 10% annually

Suppose they invested P amount initially

So, compound interest, compounded monthly is

$\Rightarrow A=P\left( 1+\frac{r}{n}\right)^{nt}\quad [\text{n=Numner of compounding periods}]\\\\\text{Insert the values}\\\Rightarrow 64,000=P\left( 1+\frac{0.10}{12}\right)^{12\times 3}\\\\\Rightarrow 64,000=P\left( 1+\frac{10}{12}\right)^{36}\\\\\Rightarrow P=\dfrac{64000}{1.3481}\\\\\Rightarrow P=\$\ 47,471.37\approx \$ 47,471$

Mathematics

Step-by-step answer

P Answered by Specialist

$\$47,471$

Step-by-step explanation:

Given

Julien's parents want $64,000 at the end of 3 years

The rate of interest is 10% annually

Suppose they invested P amount initially

So, compound interest, compounded monthly is

StudenGPT

Question Attempt: 1 of 1 Time Remaining: 29:41 9 10 Last year, Ahmad opened an investment account with . At the end of the year, the amount in the account had increased by . How much is this increase in dollars? How much money was in his account at the end of last year? begin{tabular}{|lr|} hline Increase in amount: & Year-end amount: & hline end{tabular}

Step-by-step answer

P Answered by Studen AI

Read the question carefully to determine what is asked. The question provides that Ahmad originally had $5800 in his investment account. The amount in the account increased by 6.5% over the year. We are asked to calculate the increase in dollars and the total amount in his account at the end of the year.

Let's solve this step by step.

Step 1: Calculate the increase in the account.

The increase in Ahmad’s account is given as a percentage (6.5%). To find out how much this percentage represents in dollars, we need to calculate 6.5% of $5800.

A percentage is simply a fraction of 100. So, 6.5% is the same as 6.5/100 or 0.065. To calculate the percentage of a number, we can multiply that number by the percentage as a decimal.

Hence,
Increase = $5800 * 6.5/100

Hence,
Increase = $5800 * 0.065

Calculate the above multiplication to get the increase amount.

Step 2: Calculate the total amount in the account at the end of the year.

After finding out the increase, add this amount to the original principal ($5800) to calculate total amount at end of year.

Hence,
Total amount at year-end = Original amount + Increase

Substitute "Original amount" with $5800 and "Increase" with the value from Step 1 calculation.

Hence,
Total amount at year-end = $5800 + Increase

Calculate to get total amount.

Finally, check your work by ensuring your solution makes sense in the context of the initial problem and by plugging your solution back into the initial problem, if possible.

If at any point you made a mistake, go through each step again to find and fix errors.

Please note also that in math, especially when solving a word problem like this, it’s important to also consider the context of the problem. Does your answer make sense? Is it reasonable to the situation? If your answer seems off, you may want to double-check your work to make sure you didn’t make a mistake somewhere in your calculations.

This careful systematic approach and check-back ensures minimizing errors.

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