Unit 8 – Personal Finance Compound Interest Formula

Question for thought You invest $1000 at a rate of 12% per year. If you get interest every month, how much should you get at the end of the first month?

Compound Interest Formula Where: A = Total Amount of investment (or Future Value) P = Principal (or Present Value) i = interest rate as a decimal, per compounding period n = total number of compounding periods Or

Interest Formula “i“ and “n” are both dependent upon the compounding period:

Interest Compounded # of Compounding Periods in Annually (once a year) 1Interest rate given# of years given Semi-annually (twice a year) 2Interest rate ÷ 2(# of years) x 2 Quarterly (4 times a year) 4Interest rate ÷ 4(# of years) x 4 Bi-Monthly (every other month) 6Interest rate ÷ 6(# of years) x 6 Monthly (12 times a year) 12Interest rate ÷ 12(# of years) x 12 Semi-Monthly (twice a month) 24Interest rate ÷ 24(# of years) x 24 Bi-Weekly (every 2 weeks) 26Interest rate ÷ 26(# of years) x 26 Weekly (once a week) 52Interest rate ÷ 52(# of years) x 52 Daily (once a day) 365Interest rate ÷ 365(# of years) x 365

Example 1 Calculate the amount of the investment if $500 is invested at 3% compounded quarterly for 3 years. A=?, P=500,, n=3×4=12 The amount of the investment after three years is $546.90

Example 2 Jack borrowed $8000 to start a small business. The interest rate on the loan was 10% per year, compounded monthly. He is expected to repay the loan in full after 5 years. How much must Jack repay? How much of the amount Jack repays will be interest?

Solution How much must Jack repay? A=?, P=8000,, n=5×12=60 Jack will have to repay $13,162.47

Solution How much of the amount Jack repays will be interest? Interest Paid = A-P Interest Paid = $13, $8000 Interest Paid = $5, Jack will pay $ in interest