Interest is what you pay each year to borrow money, or what you get when someone, such as a bank, uses yours. When you're shopping for loans or places to save money, though, you need to look beyond merely a simple interest rate. To gauge the true costs of borrowing money -- or the true return on your interest -- you need to grasp the different types of interest rates and formulas used by banks, mortgage firms and credit card companies.

## When You're Borrowing

**Amortization**

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Your interest rate determines how your loan is amortized -- and how long it takes to pay it off. In this process, you make equal payments that are distributed between reducing what you owe and interest. As the loan gets older, you pay less in interest and decrease your principal faster. For instance, suppose you borrow $100,000 at 6 percent interest per year and have 10 yearly payments of $13,586.80. In year one, interest takes $6,000 of your payment and $7,586.80 goes to principal, but in the last year, $12,048.67 goes to principal and $769.06 to interest.

## The True Borrowing Cost

The **annual percentage rate** represents what it really, or effectively, costs you to borrow money or get credit. It depends on the finance charges associated with the loan or credit card. Lenders must count as finance charges interest and charges imposed on a borrower to get the loan, such as:

- Mortgage broker fees
- Loan origination fees
- Premiums for credit guarantee insurance
- Points the lender must pay
- Property or liability insurance premiums if the borrower doesn't select the company
- Appraisal and credit report fees, unless all applicants are charged or unless the loan is secured by real property, such as a residential mortgage

## Figuring the APR

You can perform your own annual percentage rate calculation with the formula APR=2nr/(n+1), with

"n" representing the total number of payments

"r" representing the annual interest rate

For example, you ponder buying a $28,505 car and taking out a loan with 60 monthly payments of $631. To get the annual percentage rate:

Figure the interest by multiplying 60 by $631 and subtracting from it $28,505 to get interest of $9,355

Divide $9,355 (the interest amount) by the product of 5 years and $28,505 to get an interest rate of 6.56 percent

Using APR=2nr/(n+1), enter 60 for "n" and 0.065 for "r" to get an APR of 12.91 percent.

## When You're Saving

Use the **annual percentage yield** when you're shopping for a place to build your nest egg. This rate depends on what your financial institution says is the interest rate and how often interest is compounded. In essence, you're converting a stated rate for interest that is compounded less than yearly to an annual rate. The Consumer Finance Protection Bureau requires banks to state the interest as an annual rate.

**Calculating the Rate**

The formula used by the government is APY=100 x [(1+interest paid/principal) x (365/Days in the term)-1]. For example, if you deposit $1,000 on a one-year certificate of deposit and it earns $61.68 interest, the APY is 6.17 percent. In this formula, enter 182 days if you have a six- month certificate of deposit.

**Calculating the Growth**

To determine what you'll get from a given annual percentage yield, use this formula: F=D x (1+r)^{t}, where

- "F" means the future value, or what you'll have in the account at the end
- "D" represents your deposit,
- "r" is the interest rate
- "t" is the number of years you hold the account

For example, you put $5,500 into a three-year certificate of deposit with an annual percentage rate of 6.608 percent. At the end, your account will be worth $6,663.96, which you get by inputing $5,500 for "D," 0.0608 for "r" and the number "3" for "t."

- Federal Deposit Insurance Corporation: Law, Regulation,
- Consumer Finance Protection Bureau: What is the Difference Between Interest Rate an Annual Percentage Rate
- Consumer Finance Protection Bureau: What is Negaive Amortization?
- California State Board of Equalization: Time Value of Money - Six Functions of a Dollar: Lesson 7 -- Periodic Repayment
- University of Nebraska - Lincoln: NebGuide: Figuring the True Cost (APR) of Credit
- Consumer Finance Protection Bureau: CFPB Consumer Laws and Regulations -- Truth in Lending Act
- Austin Peay State University: Math 1010 -- The Mathematics of Finance -- Credit Cards and Consumer Loans
- University of Arizona: Compound Interest and APY