Diamond
Active Member
Interest Calculations
Table of Contents:
1. Guide Preamble
2. Types of Interest
3. Examples
1. Guide Preamble
2. Types of Interest
3. Examples
Guide Preamble: This guide is mainly about how to calculate interest on money. The guide is best for those who have completed math AB, math B or pre-calculus. Basically, what you are reading is based upon specific interest calculations, which can all be held to the same standard at any bank. The are two specific formulas depending on the type of interest. The guide will show you how much money you would have to invest to achieve a certain amount of money through interest or it can show you the amount of money which you would owe after a specific loan. It all sounds like a lot at the moment, but I assure you I will make it easy to learn. I know there are members, like myself, who are looking for ways to earn money and those who are associated with banking.
Types of Interest:
- Continuous Interest- This is the formula which you will be using for most types of interest calculations. (A = Pe^rt)
A= amount (This is the final amount, or what you will end up with; usually in terms of dollars.)
P= principal (This is the initial amount of a specified object, or what you start with; usually in terms of dollars.)
e= is a constant which is actually a number which can be located on our calculator. I will show you how to use this specific term inside of an equation.
^= any time this term is used it means raised to the power of whatever number is next to it. So in this scenario it stands for e raised to the rt power, pretty simple.
r= rate of interest; sometimes listed as "i" (The rate of interest is usually a number less than 15 because anything higher would be a ridiculous interest rate and usually not likely. The interest rate is listed in percentages such as 8% interest.
t= time (The time, usually in years, of which the interest rate is active for.
- Compound Interest- This formula is a much better interest plan than normal interest. If you are planning on engaging in a deal for a loan you would rather be using regular interest. If you are putting money in the bank to accumulate you're going to want compound interest. (A = P[1+(i/n)]^nt)
A= amount.
P= principal.
i= rate of interest.
t= time.
n= the frequency of compound in one year (This number is usually one of the following: 1, 4, 12, 52, or 365. These numbers each represent a specific amount of days. 1 is compounding one time per year. 4 is compounding quarterly or every 3 months. 12 is compounding every month. 52 is compounding every week. Lastly, 365 is compounding every day.)
Examples:
Ex. 1: Continuous Interest (Solving for P)- Mark wants to accumulate $30,000 for the down payment on the house she would like to buy in 5 years. How much money must she invest today to reach her goal of $30,000 if she can earn 6% per year, compounded continuously?
- Breakdown- First of you are going to need to choose the correct formula. Since the problem says "compounded continuously" you will use the first formula which is A = Pe^rt. We will be solving for P, because that is the only information we aren't given. Now we will need to plug in the numbers which appear in the problem. Refer back to the top to find out which numbers go where. The rest you will be able to see below.
Note you can plug the "e" directly into your calculator.
Ex. 2: Continuous Interest (Solving for A)- What is the amount that a deposit of $1,000 will grow to in 3 years using an interest rate of 8%, compounded continuously?
- Breakdown- First of you are going to need to choose the correct formula. Since the problem says "compounded continuously" you will use the first formula which is A = Pe^rt. We will be solving for A, because that is the only information we aren't given. Now we will need to plug in the numbers which appear in the problem. Refer back to the top to find out which numbers go where. The rest you will be able to see below.
Ex. 3: Compound Interest (Solving for A)- James receives a loan of $6,300 from the NCS Bank. The loan must be repaid after 5 years at 4% per year, compounded monthly. How much will James owe the bank?
- Breakdown- First off you are going to need to establish which formula you should use. Since it says compounded monthly you are going to use the compound interest formula which is (A = P[1+(i/n)]^nt). If you refer above to "n" you will notice that monthly = 12. So wherever there is an "n", you must plug in 12. We will be solving for A because P is given to us.
Ex. 3: Compound Interest (Solving for A)- This problem is to make things simpler for those trying to comprehend it. Ok so here's our problem. R33l has $1500 and he wants to get a loan from his local bank to create a new educational website about saxophones. The bank tells him they will lend him the money, but he must repay them after 3 years at 7% per year, compounded quarterly. How much will R33l owe the local bank?
- Breakdown- First off you are going to need to establish which formula you should use. Since it says compounded monthly you are going to use the compound interest formula which is (A = P[1+(i/n)]^nt). If you refer above to "n" you will notice that quarterly = 4. So wherever there is an "n", you must plug in 4. We will be solving for A because P is given to us.
I hope that everyone enjoyed the guide and if there are any questions please feel free to ask. If you need any formulas worked out, I can help.
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