GMAT Math : Calculating compound interest

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Example Questions

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Example Question #1 : Calculating Compound Interest

Grandpa Jack wants to help his grandson, Little Jack, with college expenses. Little Jack is currently 3 years old. If Grandpa Jack invests $5,000 in a college savings account earning 5% compounded yearly, how much money will he have in 15 years when Little Jack is 18? 

Possible Answers:

Between $10,000-$10,500

 Between $9,000-$9,500 

 Between $10,500-$11,000 

 Between $9,500-$10,000 

 Between $11,000-$11,500 

Correct answer:

Between $10,000-$10,500

Explanation:

To solve this, we can create an equation for the value based on time. So if we let t be the nmbers of years that have passed, we can create a function f(t) for the value in the savings account. 

We note that f(0) =5000. (We invest 5000 at time 0.) Next year, he will have 5% more than that. To find our total value at the end of the year, we multiply 5,000 * 1.05 = 5,250. f(1) = 5000(1.05)=5,250. At the end of year 2, we will have a 5% growth rate. In other words, f(2) = (1.05)* f(1). We can rewrite this as  . We can begin to see the proper equation is . If we plug in t = 15, we will have our account balance at the end of 15 years. So, our answer is .

 

 

Example Question #2 : Calculating Compound Interest

Cherry invested  dollars in a fund that paid 6% annual interest, compounded monthly. Which of the following represents the value, in dollars, of Cherry’s investment plus interest at the end of 3 years?

Possible Answers:

 

Correct answer:

 

Explanation:

The monthly rate is 

3 years = 36 months

According to the compound interest formula

and here , , , so we can plug into the formula and get the value

Example Question #3 : Calculating Compound Interest

Scott wants to invest $1000 for 1 year. At Bank A, his investment will collect 3% interest compounded daily while at Bank B, his investment will collect 3.50% interest compounded monthly. Which bank offers a better return? How much more will he receive by choosing that bank over the other?

Possible Answers:

Correct answer:

Explanation:

Calculate the total amount from each bank using the following formula:

Bank A:

Bank B:

 

Example Question #4 : Calculating Compound Interest

Bryan invests $8,000 in both a savings account that pays 3% simple interest annually and a certificate of deposit that pays 8% simple interest anually. After the first year, Bryan has earned a total of $365.00 from these investments. How much did Bryan invest in the certificate of deposit?

Possible Answers:

Correct answer:

Explanation:

Let  be the amount Bryan invested in the certificate of deposit. Then he deposited  in a savings account. 8% of the amount in the certificate of deposit is , and 3% of the amount in the savings account is ; add these interest amounts to get $365.00.  Therefore, we can set up and solve the equation:

Example Question #5 : Calculating Compound Interest

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

Possible Answers:

Correct answer:

Explanation:

Use the compound interest formula

substituting  (principal, or amount invested),  (decimal equivalent of the 8% interest rate),  (four quarters per year),  (one year).

Subtract 9,000 from this figure - the interest earned is $741.89

Example Question #6 : Calculating Compound Interest

Tom deposits his $10,000 inheritance in a savings account with a 4% annual interest rate, compounded quarterly. He leaves it there untouched for six months, after which he withdraws $5,000. He leaves the remainder untouched for another six months.

How much interest has Tom earned on the inheritance after one year?

Possible Answers:

Correct answer:

Explanation:

Since in each case the interest is compounded quarterly, the annual interest rate of 4% is divided by 4 to get 1%, the effective quarterly interest rate. 

The $10,000 remains in the savings account six months, or two quarters, so 1% is added twice - equivalently, the $10,000 is multiplied by 1.01 twice:

$5,000 is withdrawn from the savings account, leaving 

This money is untouched for six months, or two quarters, so again, we multiply by 1.01 twice:

Subtract $5,000 to get the interest:

Example Question #7 : Calculating Compound Interest

On January 1, Gary borrows $10,000 to purchase an automobile at 12% annual interest, compounded quarterly beginning on April 1. He agrees to pay $800 per month on the last day of the month, beginning on January 31, over twelve months; his thirteenth payment, on the following January 31, will be the unpaid balance. How much will that thirteenth payment be?

Possible Answers:

Correct answer:

Explanation:

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

Over the course of one quarter, Gary pays off , and the remainder of the loan accruses 3% interest. This happens four times, so we will subtract $2,400 and subsequently multiply by 1.03 (adding 3% interest) four times. 

First quarter:

Second quarter:

Third quarter:

Fourth quarter:

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

Example Question #8 : Calculating Compound Interest

Jessica deposits $5,000 in a savings account at 6% interest. The interest is compounded monthly. How much will she have in her savings account after 5 years?

Possible Answers:

None of the other answers are 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.

Example Question #9 : Calculating Compound Interest

A real estate company is considering whether to accept a loan offer in order to develop property.  The principal amount of the loan is $400,000, and the annual interest rate is 7% compounded semi-anually. If the company accepts the loan, what will be the balance after 4 years?

Possible Answers:

Correct answer:

Explanation:

Recall the formula for compound interest:

, where n is the number of periods per year, r is the annual interest rate, and t is the number of years.

Plug in the values given in the question:

Example Question #10 : Calculating Compound Interest

Nick found a once-in-a-lifetime opportunity to buy a rare arcade game being sold at a garage sale for $5730. However, Nick can't afford that right now, and decides to take out a loan for $1000. Nick didn't really read the fine print on the loan, and later figures out that the loan has a 30% annualy compounded interest rate! (A very dangerous rate). How much does Nick owe on the loan 2 years from the time he takes out the loan? (Assume he's lazy and doesn't pay anything back over those 2 years.)

Possible Answers:

Correct answer:

Explanation:

For compound interest, the amount Nick owes is

 

 

where  is the principal, or starting amount of the loan ($1000),  is the interest rate per year (30% = .3). and  is the time that has passed since Nick took out the loan. (2)

 

We have

 

Hence our answer is $1690.

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