# Algebra II : Interest Equations

## Example Questions

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Catherine invests $3500 in an investment account. The account earns 10% interest, compounded quarterly. After 5 years, how much money will she have? Possible Answers: Correct answer: Explanation: The formula for calculating the future value of an interest earning account is , where = future value, = present value, = annual interest rate, = number of times the interest is compounded per year, and = the number of years that have passed. The problem asks for the amount of money in the account after 5 years, with 10% interested compounded four times per year (quarterly). Plug in the given quantities and simplify: ### Example Question #2 : Interest Equations Felicia put money in a saving account with a 5% interest rate, compounded annually. After five years, she had$10,000. How much was her initial investment?

Explanation:

The formula for finding the future value of an investment is

,

where

= future value,

= present value,

= interest rate, and

= number of times interest is compounded.

Plug in the given numbers and solve for the present value:

Jamie deposits $5000 into an account at ABC bank. The account will earn a 4% interest rate compounded yearly. Jamie would like to withdraw the accumulated amount after 5 years and close the account. How much money would Jamie withdraw after 5 years? (Round your answer to the nearest dollar) Possible Answers: Correct answer: Explanation: Initial amount = 5000 The account earns 4% compounded yearly ===> Each$1.00 will grow into $1.04. Growth rate = 1.04 Jamie will withdraw the money after 5 years. Since the interest is compounded yearly, the number of periods is equal to the number of years the money will be in the account. number of periods = 5 From the above information, we can calculate the amount accumulated (or final amount) after 5 years using the following formula: final amount = initial amount * (growth rate)number of periods ### Example Question #4 : Interest Equations Round the answer to two decimals. Anthony put , in his savings account today. The bank pays interest of every year. How much does he have in his savings account after years? Possible Answers: Correct answer: Explanation: The formula for computing interest is: Beginning Amount x ((1 + rate)^number of years) = Ending Amount After number of years Make sure to convert the rate from percent to number: 3% = 0.03 So the answer is ### Example Question #5 : Interest Equations For coninuous compound interest: Where If an initial deposit of is continuously compounded at a rate of for years, what will be the final principal value to the nearest dollar? Possible Answers: None of the other answers. Correct answer: Explanation: Using the equation for continuous compound interest and the given information, we get ### Example Question #6 : Interest Equations Remember If an account has a starting principle P =$5,000, an interest rate r = 12% or 0.12, compounded annually, how much money should there be after five years? Assume no money has been added or taken out of the account since it was opened.

Explanation:

is the compound interest formula where

P = Initial deposit = 5000

r = Interest rate = 0.12

n = Number of times interest is compounded per year = 1

t = Number of years that have passed = 5

Round to the nearest cent or hundredth is .

Julio invests $5000 into an account with a 2.5% interest rate, compounded quarterly. What is his account balance after 1 year (rounded to the nearest cent)? Possible Answers: Correct answer: Explanation: To determine Julio's account balance, we must use the interest formula given below: where P is his principal (initial) investment, r is the interest rate (as a decimal), n is the number of times the interest is compounded, and t is the amount of time elapsed. Plugging in all of our given information into the above formula - knowing that quarterly means four times a year - we get ### Example Question #8 : Interest Equations Martisha invests$2000 into an account with continuously compounded interest. The account has an interest rate of 2.5%. Find the balance of the account after 2 years, rounded to the nearest cent.

Explanation:

To find the balance, B, of a continuously compounded interest account after a certain amount of time, we must use the following formula:

, where P is the initial investment, r is the interest rate (as a decimal), and t is the amount of time being considered.

Plugging in all of the given information, we get

which rounded becomes \$2102.54

### Example Question #9 : Interest Equations

How long will it take for Nikki to triple her initial investment into a continuously compounded interest account with an interest rate of 1.9%?

We are not given enough information to solve the problem

0.5782 years

0.214 years

57.82 years

57.82 years

Explanation:

The formula to find the balance, B, of a continuously compounded interest account with interest rate, r, after a certain time, t, is given by

To solve this problem, we need to know only the initial investment (P), our final balance (three times P) and the interest rate (expressed as a decimal), 0.019.

Plugging in our known information into the formula for continuously compounded interest, we get

We now solve for t:

Exponentiating both sides allows us to get rid of the exponential:

### Example Question #10 : Interest Equations

Sheila wants to double her initial investment into a compounded interest account, with an interest rate of 4%. How long will this take, if the interest is compounded annually?

0.0565 years

17.67 years

0.52 years

1.923 years

17.67 years

Explanation:

To determine the amount of time needed to double the initial investment - P - into a compound interest account, we simply plug in our given information into the formula:

where B is the balance, P is the initial investment, r is the interest rate (as a decimal), n is the number of times the interest is compounded, and t is the time elapsed.

Now, because we are doubling P, our balance B becomes two times P:

Now, we can solve for P:

To bring the time variable down from being an exponent, we take the logarithm of both sides (common or natural):

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