GMAT Math help » Problem-Solving concerns » Word troubles » Interest problems » Calculating compound attention

Grandpa Jack wants to aid his grandson, tiny Jack, through college expenses. Tiny Jack is right now 3 year old. If Grandpa Jack invests $5,000 in a university savings account earning 5% compounded yearly, exactly how much money will he have actually in 15 years when tiny Jack is 18? 


Explanation:

To fix this, us can create an equation because that the value based on time. Therefore if we let t be the nmbers of years that have passed, we can create a role f(t) for the value in the to save account. 

We note that f(0) =5000. (We invest 5000 in ~ time 0.) following year, the will have 5% more than that. To discover our complete value at the finish of the year, we multiply 5,000 * 1.05 = 5,250. F(1) = 5000(1.05)=5,250. In ~ the finish of year 2, us will have actually a 5% growth rate. In other words, f(2) = (1.05)* f(1). We deserve to rewrite this as 

*
 . Us can start to watch the proper equation is 
*
. If we plugin t = 15, we will have our account balance at the end of 15 years. So, ours answer is 
*
.

You are watching: John inherited 5000 from his grandfather

 

 


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Example inquiry #2 : Calculating Compound interest


Cherry invested 

*
dollars in a fund that payment 6% yearly interest, compounded monthly. I m sorry of the following represents the value, in dollars, the Cherry’s invest plus attention at the finish of 3 years?


Possible Answers:

 


*


*


*


*


Correct answer:

 


Explanation:

The monthly price is 

*

3 year = 36 month

According to the compound attention formula

*

and here

*
,
*
,
*
, so we have the right to plug right into the formula and also get the value

*


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Example question #3 : Calculating Compound interest


Scott desires to invest $1000 for 1 year. At bank A, his investment will certainly collect 3% interest compounded daily while at bank B, his investment will certainly collect 3.50% interest compounded monthly. Which bank offers a much better return? how much an ext will he get by selecting that financial institution over the other?


Possible Answers:
Correct answer:

*


Explanation:

Calculate the total amount from each bank using the complying with formula:

*

Bank A:

*

Bank B:

*

*

 


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Example inquiry #4 : Calculating Compound attention


Bryan invests $8,000 in both a save account the pays 3% straightforward interest annually and also a certificate that deposit that pays 8% straightforward interest anually. ~ the very first year, Bryan has earned a full of $365.00 from these investments. Exactly how much did Bryan invest in the certificate the deposit?


Possible Answers:
Correct answer:

*


Explanation:

Let 

*
 be the amount Bryan invest in the certificate the deposit. Then he deposited 
*
 in a save account. 8% that the quantity in the certificate that deposit is 
*
, and also 3% of the quantity in the save account is 
*
; add these interest amounts to get $365.00. Therefore, we can collection up and solve the equation:

*

*

*

*

*

*

*


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Example concern #5 : Calculating Compound interest


Barry invests $9000 in corporate bonds at 8% annual interest, compounded quarterly. In ~ the end of the year, how much interest has actually his invest earned?


Possible Answers:
Correct answer:

*


Explanation:

Use the compound attention formula

*

substituting 

*
 (principal, or lot invested), 
*
 (decimal equivalent of the 8% attention rate), 
*
 (four soldier per year), 
*
 (one year).

*

*

*

Subtract 9,000 indigenous this number - the attention earned is $741.89


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Example inquiry #6 : Calculating Compound attention


Tom deposits his $10,000 inheritance in a to save account through a 4% annual interest rate, compounded quarterly. He pipeline it over there untouched for six months, after which that withdraws $5,000. He leaves the remainder untouched for an additional six months.

How lot interest has Tom earn on the inheritance after one year?


Possible Answers:
Correct answer:

*


Explanation:

Since in each case the interest is compounded quarterly, the annual interest price of 4% is separated by 4 to gain 1%, the reliable quarterly interest rate. 

The $10,000 continues to be in the to save account 6 months, or 2 quarters, for this reason 1% is included twice - equivalently, the $10,000 is multiply by 1.01 twice:

*

*

$5,000 is withdrawn indigenous the to save account, leaving 

*

This money is untouched for six months, or 2 quarters, therefore again, us multiply by 1.01 twice:

*

*

Subtract $5,000 to gain the interest:

*


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Example concern #7 : Calculating Compound attention


On January 1, Gary borrows $10,000 to purchase an automobile at 12% annual interest, compounded quarterly start on April 1. The agrees to pay $800 per month ~ above the critical day of the month, beginning on January 31, over twelve months; his thirteenth payment, top top the complying with January 31, will certainly be the unpaid balance. Just how much will that thirteenth payment be?


Possible Answers:
Correct answer:

*


Explanation:

12% yearly interest compounded quarterly is, effectively, 3% attention per quarter.

Over the course of one quarter, Gary payment off 

*
, and also the remainder that the loan accruses 3% interest. This happens four times, so we will certainly subtract $2,400 and also subsequently multiply by 1.03 (adding 3% interest) four times. 

First quarter:

*

*

Second quarter:

*

*

Third quarter:

*

*

Fourth quarter:

*

*

The thriteenth payment, through which Gary will pay off the loan, will be $913.16.


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Example question #8 : Calculating Compound interest


Jessica deposits $5,000 in a savings account at 6% interest. The interest is compounded monthly. Just how much will certainly she have in she savings account ~ 5 years?


Possible Answers:

None the the various other answers space correct.


Correct answer:

*


Explanation:

*

where 

*
is the principal, 
*
is the number of times per year interest is compounded, 
*
is the time in years, and 
*
is the interest rate.

*


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Example concern #9 : Calculating Compound interest


A actual estate firm is considering even if it is to accept a loan sell in bespeak to build property. The primary amount of the loan is $400,000, and the annual interest price is 7% compounded semi-anually. If the firm accepts the loan, what will certainly be the balance after 4 years?


Possible Answers:
Correct answer:

*


Explanation:

Recall the formula for link interest:

*
, wherein n is the variety of periods every year, r is the yearly interest rate, and also t is the variety of years.

Plug in the values offered in the question:

*

*


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Example concern #10 : Calculating Compound attention


Nick found a once-in-a-lifetime possibility to buy a rare arcade game being marketed at a garage sale for $5730. However, Nick can"t bought that appropriate now, and also decides come take out a loan for $1000. Nick didn"t really read the fine print on the loan, and also later figures out the the loan has a 30% annualy compounded attention rate! (A really dangerous rate). How much walk Nick owe on the loan 2 year from the moment he takes the end the loan? (Assume he"s lazy and doesn"t salary anything earlier over those 2 years.)


Possible Answers:
Correct answer:

*


Explanation:

For compound interest, the lot Nick owes is

 

*

 

where 

*
 is the principal, or starting amount the the loan ($1000), 
*
 is the interest rate per year (30% = .3). And 
*
 is the moment that has passed because Nick took the end the loan. (2)

 

We have

 

*

Hence our answer is $1690.

See more: How To Throw A Screwball With A Wiffle Ball, Throw Wiffle Ball Pitches


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