Financial Applications -Compound Interest Choi

What is Compound Interest? Recall: Simple Interest – Interest is earned on the original sum of money invested. Any interest previously earned does not earn interest. Compound Interest – Interest is reinvested at regular intervals. The interest is added to the principal to earn interest for the next interval of time, or compounding period.

Simple vs Compound Interest If you invest $100 and get interest 10% per year, Simple Interest You will have ______ in 1 year. $110 ______ in 2 years. $120 ______ in 3 years. $130 Compound Interest You will have ______ in 1 year. $110 ______ in 2 years. $121 $110 + (10% of $110)  ______ in 3 years. $133.1 $121 + (10% of $121) 

Compound Interest formula The formula used in compound interest is Amount (A) . Principal (P) Interest rate per period (i) Number of compounding periods involved (n)

Compound periods Number of compounding periods depends on how many times per year the interest is compounded. How often interest is compounded Effective Rate r = annual interest rate # of compounding periods in t years Annually Once / year i = r n = t Semi-annually Twice / year i = r / 2 n = 2t Quarterly 4 times / year i = r / 4 n = 4t Monthly 12 times / year i = r / 12 n = 12t Daily 365 times / year i = r / 365 n = 365t

Example 1 – Compound Interest To take a technology course, Mark borrows $3000 at an interest rate of 4.75% per annum, compounded annually. He plans to pay back the loan in 5 years. a) How much will Mark owe after 5 years? b) How much interest will Mark pay for the loan? Compounded annually Therefore, Mark will owe $3783.48 after 5 years. b) Interest: (Cost of borrow) =$3783.48 - $3000 =$783.48

Example 2 – Compound Interest $10000 is invested for five years at 6% per annum compounded semi- annually. a) Determine the amount of the investment at the end of the 5 years. b) Determine the interest earned in the five years. Compounded semi-annually Therefore, the amount of the investment will be $13439.16 after 5 years. b) Interest earned: =$13439.16 - $10000 =$3439.16 10 semi-annuals in 5 years

Example 3 – Compound Interest Joe buys a new sofa priced at $800. He can pay $800 now or not make any payment now and pay $950 in one year. The salesperson tells Joe that in effect he will have a loan of $800 for one year, compounded monthly. What is the monthly interest rate that Joe would be paying? or Therefore, the monthly interest rate (i) is 1.44%;. Compounded monthly and the annual interest rate (r) is 17.3% per annum. 12 months in 1 year

Example 4 – Finding the Period Approximately how long would it take for a $15000 investment to double if it earns 15.6%/annum interest compounded weekly? or Therefore, it will take approx. 231.40 weeks or Compounded weekly approx. 4.45 years to double!! 52 weeks in 1 year

Recall: Simple vs Compound Interest If you invest $100 and get interest 10% per year, Simple Interest You will have ______ in 1 year. $110 ______ in 2 years. $120 ______ in 3 years. $130 Compound Interest You will have ______ in 1 year. $110 ______ in 2 years. $121 $110 + (10% of $110)  ______ in 3 years. $133.1 $121 + (10% of $121)  Using the formula

Homework: WS: Compound Interest