Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?
600
720
1080
1200
1440

3 weeks ago

Solution 1

Guest Guest #7253123
3 weeks ago

Julie put half of her savings in a savings account. The amount of Julie initial saving in both accounts is 1200.

Since simple interest is calculated only on the principal, the simple interest income per year will be half of the simple interest income after two years. So a simple interest account earns $60 in the first year and another $60 in the second year.

In the second year, the compound interest account will earn the remaining $66, while the simple interest account will only earn $60. The difference of $6 between simple and compound interest earned on the same amount two years later is due to the interest earned in compound interest.

Calculating the problem:

Now, calculate the interest rate using the interest earned on interest for the compound interest account.

The $6 interest earned on the interest was calculated out of the total interest earned on the first year, which is 60$.

Divide 6 by 60 to find the interest rate: (6 ÷ 60) x 100 = 10%.

Given that interest rate is 10%, Julie's investment in the simple interest account is

Interest = Principal x Rate x Time

120 = P x 10% x 2

120 = P x 20%

120 = P x 20/100

P = 120 x 100/20

P = 600

Hence, the initial investment in both accounts was 1200 (600 + 600).

Simple interest:

Simple interest is calculated by multiplying the daily interest rate by the principal amount by the number of days until the next payment. Simple interest benefits consumers who pay their loans on time or at the beginning of each month. Auto loans and short-term personal loans are usually simple interest loans.

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📚 Related Questions

Question
Anna took out a $10,000 loan to pay tuition fees. How much will she owe after one year, if she does not make any payments and her bank charges 10% annual interest, compounded semiannually?
11,000
11025
11075
11200
11250
Solution 1

The amount Anna will owe if she doesn't make any payments and her bank charges 10% annual interest compounded semiannually = $11,025

Option B is correct .

What is simple interest?

Simple interest is a quick and easy way to calculate interest on a loan. Simple interest is the daily interest rate multiplied by the principal multiplied by the number of days until the next payment. This type of interest is typically applied to auto and short-term loans, but some mortgages use this method of calculation.

Evaluating the simple interest :

Compound interest is calculated on the principal plus interest already accrued.

Balance= P[tex](1+r/n)^{t}[/tex]

, where

P = Principal,

r = Interest rate (in %),

n = number of times per year,

t = number of years.

Calculate the simple interest given terms, add it to the principal,

Calculates simple interest and adds it to the principal,

Simple interest = Principal Amount x Interest Rate x Time

                      Simple interest = 10,000 x 10/100 x 1

                                  Simple interest = 10,000 x 1/10

                                        Simple interest = 1000

Now add simple interest to the principal amount to find the balance after one year.

                                     Balance = 10,000 + 1000

                                                 Balance = 11000

After compounding the interest, the balance after one year will be 11,000. Compound interest is only slightly more than simple interest,

Add 5% to the principal to find the balance after 6 months, then add another 5% calculated from the new balance.

Balance after 6 months = 10,500

Add 5% of 10,500:

                                             10,500 + 5%10,500

                                                = 10,500 + 525

                                                         = 11,025.

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Question
Nathan deposited $4,500 into a savings account that pays 8% annual interest, compounded quarterly. Which of the following is the best approximation of the interest will he earn in one year if he does not make any further deposits or withdrawals from this account?
360
371
752
1083
1445
Solution 1

Nathan deposited $4,500 into a savings account . The interest he earn in 1 year is 360

Calculating the problem:

Compound interest is calculated on the principal amount, as well as on any interest already earned.

P = Principal, r = Interest rate (in %), n = number of times per year, t = number of years.

Simple interest = Principal Amount x Interest Rate x Time

Simple interest = 4500 x 8/100 x 1

Simple interest = 45 x 8

Simple interest = 360

How can I make money with compound interest?

Compound interest is calculated by multiplying the initial principal amount by 1 and adding the annual interest rate minus the number of compounding periods. After that, the total amount of the first loan is subtracted from the resulting value.Compound interest is adding interest to the principal of a loan or deposit, i.e. principal plus interest.

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Question
Compound interest is calculated on the principal, as well as on any interest already earned. Use compound interest when the question explicitly uses the term "Compound".
Example:
John takes out a $10,000 loan at an annual interest of 12%, compounded semiannually. what will be the balance of the loan at the end of the year?
Notice the following:
1) Interest rate = 12% annual
2) Time - 1 year
3) Compound - semiannually. Interest is calculated after six months, then again at the end of the year.
Solution 1

John interest after 6 months = $10,600 and balance at the end of year = $11,236 .

Compound interest :

Compound interest is adding interest to the principal of a loan or deposit, i.e. principal plus interest. This can be done by reinvesting the interest, adding it to the principal borrowed instead of repaying it, or requiring the borrower to pay and earn interest on the principal plus previously accrued interest in the next period. Compound interest is the norm in finance and economics.

Calculating the interest amount :

Six months later, John's loan has reached half the annual interest rate, or 6%.

The balance of the loan after six months would be :

                         $10,000 + 10,000·6%

                                         = 10,600.

The remaining interest accrues on this balance at the end of the year. Another 6%.

The year-end balance sheet is as follows:

                                10,600 + 10,600·6%

                                            = $11,236.

Consider that the interest rate for every 6-month period is 6% - half of the 12% annual rate.

Interest....6%

Principal= $10,600....

                       $10,600(1+6%)

                         $10,600 + 636

                       =$11,236

Compound interest is in contrast to simple interest. With simple interest, there is no compound interest because previously accrued interest is not added to the principal for the current period. APR is the amount of interest per period multiplied by the number of periods per year.

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Question
That's pretty cool. Can I see an example?
Sure.
In the beginning of 1997, Priscilla invested $5,000 in a savings account that that pays 8% annual income, compounded quarterly. If Priscilla makes no further deposits into or withdrawals from the account, approximately how much money will she have in the account two years later, at the end of 1998?
$800
$858
$5,800
$5,858
$10,000
Solution 1

In the beginning of 1997, Priscilla invested $5,000 in a savings account. She have in the account two years later, at the end of 1998 is $5,800

Option D is correct.

Calculating the problem:

Interest rate = 8% annual

Time - 2 years

Compound - quarterly.

P = $5,000, r = 8%, n = 4 times a year (compounded quarterly), t = 2 years.

Balance after two years will be 5,000(1 + 8%/4)4×2

                                                     5,000(1.02)8.

A 8% annual simple interest on a principal of $5000 will give

                     5,000×8%

                      = 5,000 × 8 / 100

                       = 50 × 8

                        = $400 a year.

Over two year, the savings account will earn 2×$400 = $800 using simple interest, and the balance at the end of 1998 will be 5000+800 = $5800.

Why is it called compound interest?

Compound interest is interest on a deposit calculated on both the principal amount and the accumulated interest from previous periods. Or, more simply put, compound interest is interest earned on interest. Interest can be compounded according to different frequency schedules such as daily, monthly, and yearly.

Why is compound interest important?

Compound interest allows your money to grow faster because interest is calculated based on accrued interest over time, not just the original principal. Compound interest can create a snowball effect as the original investments and the income from those investments grow together.

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For interest questions, Notice the following three pieces of the puzzle:
1) Interest rate - usually given as a %
2) Time - How long the interest is calculated for.
3) Compounded - Annually, semi-annually (every six months), quarterly, monthly.
Simple Interest formula = Principal × Rate × Time
Use simple interest in the following cases:
1) The question explicitly use the phrase "simple interest"
2) The calculation time for the interest is shorter than the stated interest period. e.g. 12% annual interest calculated after a 6-month time period.
Solution 1

The above puzzle is done To Sum up the simple interest compounded annually or semi annually.

What is simple and compound interest?

Interest can be calculated in two ways: Simple interest is calculated on the principal or original amount of the loan. Compound interest may be considered "interest" because it is calculated on the principal plus interest accrued in previous periods.

What is simple interest?

Simple interest is based on the principal amount of the loan or initial deposit amount in a savings account. Simple interest earns no interest. In other words, the creditor pays interest only on the balance of the principal and the borrower does not have to pay interest on the previously accumulated interest.

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Some GMAT questions will introduce the concept of interest earned on a Principal. These questions are easily identified by the use of the term "Interest" somewhere in the question (Duh!).
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1) Interest rate - usually given as a %
2) Time - How long the interest is calculated for.
3) Compounded - Annually, semi-annually (every six months), quarterly, monthly.
Solution 1

Simple interest is calculated only on the principal.  John's loan will have incurred $600 after a six-month period.

Simple interest :

Simple interest is calculated by multiplying the daily interest rate by the principal amount by the number of days until the next payment. Simple interest benefits consumers who pay their loans on time or at the beginning of each month. Auto loans and short-term personal loans are usually simple interest loans.

Solving the puzzle given :

Simple interest is calculated only on the principal. The formula for simple interest is principal x interest rate x hours.

1) The question explicitly uses the term “simple interest”

2) The interest calculation period is shorter than the specified interest period.

Example: 12% annual interest calculated after 6 months.

Solving for 3

Example:

John takes out a $10,000 loan at an annual interest of 12%. How much interest will the loan incur after six months?

Notice the following:

1) Interest rate = 12% annual

2) Time - 6 months. Interest is an annual interest rate, so use time as a fraction of 6 months / 12 months = 1/2 year. Since the calculation period is shorter than the specified interest period, this is an indicator for using simple interest.

3) Compound interest - not mentioned - Another reason to use the simple formula.

Resolution: use the simple interest formula =

                            $10000 × 12% × ½

                             = 1200 × ½

                                  = $600.

John's loan will have incurred $600 after a six-month period.

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