All SAT Math Resources
Example Question #243 : Exponents
A five-year bond is opened with in it and an interest rate of %, compounded annually. This account is allowed to compound for five years. Which of the following most closely approximates the total amount in the account after that period of time?
Each year, you can calculate your interest by multiplying the principle () by . For one year, this would be:
For two years, it would be:
, which is the same as
Therefore, you can solve for a five year period by doing:
Using your calculator, you can expand the into a series of multiplications. This gives you , which is closest to .
Example Question #1 : How To Find Compound Interest
If a cash deposit account is opened with for a three year period at % interest compounded once annually, which of the following is closest to the positive difference of the interest accrued between the last two years and the first two years?
It is easiest to break this down into steps. For each year, you will multiply by to calculate the new value. Therefore, let's make a chart:
After year 1: ; Total interest:
After year 2: ; Let us round this to ; Total interest:
After year 3: ; Let us round this to ; Total interest:
Thus, the positive difference of the interest from the last period and the interest from the first period is:
Example Question #1 : Pattern Behaviors In Exponents
Jack has , to invest. If he invests two-thirds of it into a high-yield savings account with an annual interest rate of , compounded quarterly, and the other third in a regular savings account at simple interest, how much does Jack earn after one year?
First, break the problem into two segments: the amount Jack invests in the high-yield savings, and the amount Jack invests in the simple interest account (10,000 and 5,000 respectively).
Now let's work with the high-yield savings account. $10,000 is invested at an annual rate of 8%, compounded quarterly. We can use the compound interest formula to solve:
Plug in the values given:
Therefore, Jack makes $824.32 off his high-yield savings account. Now let's calculate the other interest:
Add the two together, and we see that Jack makes a total of, off of his investments.
Example Question #2 : Pattern Behaviors In Exponents
A truck was bought for in 2008, and it depreciates at a rate of per year. What is the value of the truck in 2016? Round to the nearest cent.
The first step is to convert the depreciation rate into a decimal. . Now lets recall the exponential decay model. , where is the starting amount of money, is the annual rate of decay, and is time (in years). After substituting, we get