Example 1: Nina deposited $800 into a savings account with an annual interest rate of 6%. If there are no withdrawals or deposits, how much money will be in the savings account after 10 years? In finance, future values of various accounts are computed using the function,, where is the future value, F(t) P is the present value (or principal), is the rate of change, and is time. However, the interest rates are almost always tied to a specific time period and only accumulate once this time period has elapsed (called In this context, we refer to the time periods as compounding periods. A compounding period is a compounding). fraction of one year. If interest is compounded monthly: How many times will interest be added per year (compounded)? 12 How would you represent this time period as a fraction of a year? Consider the questions above to complete the table below. Number of Compounded Per Descriptive Adverb Compounding Period Fraction of 1 Year Year annually 1 year 1 semi-annually 6 months 2 quarterly 3 months 4 monthly 1 12 weekly 1 week 52 daily 1 day 365 Interest rates for accounts are frequently given in terms of what is called the nominal annual percentage rate of or The phrase interest rate of 6% per year compounded monthly” means a nominal change nominal APR. “an APR of 6% compounded monthly. Typically, the nominal APR is given and the unit rate of the percent rate of change for the compounding period must be calculated. This means that the nominal APR of 6% compounded monthly will be multiplied by the fraction of the year for a monthly compounding period (i.e., or ). The resulting monthly unit rate of the percent rate of change is = 0.5% per month. Example 2: If a starting value of $800 was deposited in a bank and compounded monthly, after one month there would be dollars in the account. How much will be in the account after 2 months? After 3 months? After months? n Number of Compounding Periods Future Value Expression Future Value ($)
Example 1: Nina deposited $800 into a savings account with an annual interest rate of 6%. If there are no withdrawals or deposits, how much money will be in the savings account after 10 years? In finance, future values of various accounts are computed using the function,, where F(t) is the future value, P is the present value (or principal), is the rate of change, and is time. However, the interest rates are almost always tied to a specific time period and only accumulate once this time period has elapsed (called compounding). In this context, we refer to the time periods as compounding periods. A compounding period is a fraction of one year. If interest is compounded monthly: How many times will interest be added per year (compounded)? 12 How would you represent this time period as a fraction of a year? Consider the questions above to complete the table below. Descriptive Adverb Compounding Period Number of Compounded Per Year Fraction of 1 Year annually 1 year 1 semi-annually 6 months 2 quarterly 3 months 4 monthly 1 12 weekly 1 week 52 daily 1 day 365 Interest rates for accounts are frequently given in terms of what is called the nominal annual percentage rate of change or nominal APR. The phrase “an interest rate of 6% per year compounded monthly” means a nominal APR of 6% compounded monthly. Typically, the nominal APR is given and the unit rate of the percent rate of change for the compounding period must be calculated. This means that the nominal APR of 6% compounded monthly will be multiplied by the fraction of the year for a monthly compounding period (i.e., or ). The resulting monthly unit rate of the percent rate of change is = 0.5% per month. Example 2: If a starting value of $800 was deposited in a bank and compounded monthly, after one month there would be dollars in the account. How much will be in the account after 2 months? After 3 months? After n months? Number of Compounding Periods Future Value Expression Future Value ($)
u1t3slt17_compound_interest_sample_answers.docx