All GMAT Math Resources
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?
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?
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?
Calculate the total amount from each bank using the following formula:
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?
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?
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?
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?
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.
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?
None of the other answers are correct.
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?
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.)
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)
Hence our answer is $1690.