Compound Interest

Compound Interest and Present Value

Compound Interest and Present Value Learning Unit Objectives Compound Interest (Future Value) – The Big Picture Compare simple interest with compound interest Calculate the compound amount and interest manually. Explain and compute the effective rate

Compounding Interest (Future Value) Compounding - involves the calculation of interest periodically over the life of the loan or investment Compound interest - the interest on the principal plus the interest of prior periods Future value (compound amount) - is the final amount of the loan or investment at the end of the last period Present value - the value of a loan or investment today

Future Value of $1 at 8% for Four Periods Compounding goes from present value to future value Future Value After 4 periods $1 is worth $1.36 After 3 periods $1 is worth $1.26 After 2 periods $1 is worth $1.17 After 1 period $1 is worth $1.08 Present value $1.2597 $1.3605 $1.1664 $1.08 $1.00 Number of periods

Compounding Terms Compounding Periods Interested Calculated Compounding Annually Once a year Compounding Semiannually Every 6 months Compounding Quarterly Every 3 months Compounding Monthly Every month Compounding Daily Every day Compounding fortnightly Every two weeks

Tools for Calculating Compound Interest Number of periods (N) Number of years multiplied the number of times the interest is compounded per year Rate for each period (R) Annual interest rate divided by the number of times the interest is compounded per year If you compounded $100 for 3 years at 6% annually, semiannually, or quarterly What is N and R? Periods Rate Annually: 6% / 1 = 6% Semiannually: 6% / 2 = 3% Quarterly: 6% / 4 = 1.5% Annually: 3 x 1 = 3 Semiannually: 3 x 2 = 6 Quarterly: 3 x 4 = 12

Simple Versus Compound Interest Compounded Al Jones deposited $1,000 in a savings account for 5 years at an annual interest rate of 10%. What is Al’s simple interest and maturity value? Al Jones deposited $1,000 in a savings account for 5 years at an annual compounded rate of 10%. What is Al’s interest and compounded amount? I = P x R x T I = $1,000 x .10 x 5 I = $500 Amount of money = $1,000 + $500 = $1,500 Interest: $1,610.51 - $1,000 = $610.51

Calculating Compound Amount by Table Lookup Step 4. Multiply the table factor by the amount of the loan. Step 3. Go down the period column of the table to the number desired; look across the row to find the rate. At the intersection is the table factor Step 2. Find the rate: Annual rate divided by number of times interest is compounded in 1 year Step 1. Find the periods: Years multiplied by number of times interest is compounded in 1 year

- Future Value of $1 at Compound Interest

Calculating Compound Amount by Table Lookup Steve Smith deposited $6,000 in a savings account for 5 years at an semiannual compounded rate of 10%. What is Steve’s interest and compounded amount? N = 5 x 2 = 10 R = 10% = 5% 2 Table Factor = 1.6289 Compounded Amount: $6,000 x 1.6289 = $9,773.40 I = $9,773.40 - $6,000 = $3,773.40

Nominal and Effective Rates of Interest Nominal Rate (Stated Rate) - The rate on which the bank calculates interest. Truth in Savings Law Annual Percentage Yield Flat Rate = Interest for 1 year Principal

Compounding Interest Daily Calculate what $2,000 compounded daily for 7 years will grow to at 6%pa T = 7 years R = 6% A=P(1+r)n =$2,000 ( 1+ 0.06)7= $3,007.3