All GMAT Math Resources
Example Questions
Example Question #14 : Calculating Simple Interest
If is invested at simple annual interest rate over months, what it is the amount of interest earned over that period?
Here, we cannot apply the rate as is, since it is given for a year. We just have to divide the rate by the number of months in a year, since we are looking for a monthly rate. Therefore, the applicable rate is , now we can apply the formula and we get: or .
Example Question #13 : Interest Problems
A local credit union offers short-term loans at an annual interest rate of . If Jasmine takes out a loan for months, how much will she pay in interest?
Here we need our simple interest formula. There is no compounding, so all we need is:
= Dollar amount of interest
= Amount borrowed/invested
= Annual interest rate
= Number of years borrowed/loaned
Plug in what we know and solve for :
So, Jasmine pays in interest.
Example Question #13 : Interest Problems
We deposit today in an account paying annual simple interest, how much do we have in the account at the end of the year, provided we make no other deposit?
This is a simple interest problem, therefore, the amount of interests received is given by the formula: , where is the principal, is the number of periods and is the rate over that period. In this problem is 140,000, is 10 and is 10% or 0.1. Therefore we get or 140,000. We add the interest received to the principal, and we get the final answer of .
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?
Between $9,000-$9,500
Between $10,000-$10,500
Between $11,000-$11,500
Between $9,500-$10,000
Between $10,500-$11,000
Between $10,000-$10,500
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 #1 : 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 #1 : 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:
Bank A:
Bank B:
Example Question #1 : 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 #1 : 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 #1 : 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 #1 : 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.
First quarter:
Second quarter:
Third quarter:
Fourth quarter:
The thriteenth payment, with which Gary will pay off the loan, will be $913.16.