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 ID: 386958
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Slide1
Unit 8 – Personal Finance
Compound Interest FormulaSlide2
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?Slide3
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
OrSlide4
Interest Formula
“i“ and “n” are both dependent upon the compounding period:Slide5
Interest Compounded
# of Compounding Periods
i
n
Annually
(once a year)
1
Interest rate given
# of years given
Semi-annually
(twice a year)
2
Interest rate ÷ 2
(# of years) x 2
Quarterly
(4 times a year)
4
Interest rate ÷ 4
(# of years) x 4
Bi-Monthly
(every other month)
6
Interest rate ÷ 6
(# of years) x 6
Monthly
(12 times a year)
12
Interest rate ÷ 12
(# of years) x 12
Semi-Monthly
(twice a month)
24
Interest rate ÷ 24
(# of years) x 24
Bi-Weekly
(every 2 weeks)
26
Interest rate ÷ 26
(# of years) x 26
Weekly
(once a week)
52
Interest rate ÷ 52
(# of years) x 52
Daily
(once a day)
365
Interest rate ÷ 365
(# of years) x 365Slide6
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 $546.90Slide7
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?Slide8
Solution
How much must Jack repay?
A=?, P=8000, , n=5×12=60
Jack will have to repay $13,162.47Slide9
Solution
How much of the amount Jack repays will be interest?
Interest Paid = A-P
Interest Paid = $13,162.47-$8000
Interest Paid = $5,162.47
Jack will pay $5162.47 in interest