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Section 10.2 Compound Interest. Simple interest is generally used for loans of one year or less. For loans of more than one year, the interest paid on the money borrowed usually use compound interest.

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Section 10.2Compound Interest

Simple interest is generally used for loans of one year or less. For loans of more than one year, the interest paid on the money borrowed usually use compound interest.

Compound interest is interest calculated not only on the original principal, but also on any interest that has already been earned.


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Compound Interest Formula

The compound amount formula is

A = P * (1 + i)N

where A is the compound amount when P dollars are deposited at an interest rate of i per compounding period for N compounding periods. Because i is the interest rate per compounding period and n is the number of compounding periods per year,

i = r / n N = n * t


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Example

How much interest is earned in 6 years on $8000 deposited in an account paying 9% interest, compounded monthly?


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Example

Determine the compound amount when $2000 is deposited in an account earning an interest rate of 12%, compounded quarterly, for 10 years.

CHECK YOUR PROGRESS

Determine the compound amount when $3500 is deposited in an account earning an annual interest rate of 6%, compounded semiannually, for 5 years.


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Present Value Formula

The present value formula is

where P is the original principal invested at an interest rate of i per compounding period for N compounding periods, and A is the compound amount.


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EXAMPLE

How much money should be invested in an account that earns 8% interest, compounded quarterly, in order to have $30,000 in 5 years?


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Check your progress

How much money should be invested in an account that earns 9% interest, compounded semiannually, in order to have $20000 in 5 years?


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Inflation

Inflation is an economic condition during which there are increases in the costs of goods and services.

EXAMPLE

Suppose your annual salary today is $35,000. You want to know what an equivalent salary will be in 20 years; that is, a salary that will have the same purchasing power, if the annual inflation rate is 4%.


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Effective Interest Rate

When interest is compounded, the annual rate of interest is called the nominal rate. The effective rate is the simple interest rate that would yield the same amount of interest after one year. When a bank advertises a "7% annual interest rate compounded daily and yielding 7.25%”, the nominal interest rate is 7% and the effective rate is 7.25%.


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Formula: (1+i)N - 1

Example 10. Calculate the Effective Interest Rate

A credit union offers a certificate of deposit at an annual interest rate of 8%, compounded monthly. Find the effective rate. Round to the nearest hundredth of a percent.


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EXAMPLE 11. Compare Annual Yields

  • One bank advertised an interest rate of 6% compounded quarterly, on a certificate of deposit. Another bank advertises an interest rate of 5.85% compounded monthly. Which investment has the higher annual yield?


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