Annual compound interest monthly calculation

SI and CI are easy concept to learn. I m writing about them because someone asked me a question with little twist which I thought worth sharing

In simple interest calculation interest is charged only on the principal whereas in compound interest calculation the interest gets added with the principal and interest is charged on principal plus accumulated interest.

SI = PRT                               >> interest at particular time

SI = P x (1+RT)                    >> interest plus principal at particular time (Total Amount)

CI = P x (1+R/N) NT                   >> Total Amount

P = Principal

R = Annual rate of interest

T = Time

N = Compounding period vis Annual(1), Semi Annual(2), Quarterly(4), Monthly(12), Daily(365)

An Example

Amount = 10000

Annual Interest rate = 12%

Time = 5 yrs

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Now the twist question, at annual compounding what is the value after  69 months

No. of completed years = 5 (5 x 12 = 60)

No. of months remaining  = 9 (69 – 60)

Convert months into yearly fraction = 9/12 = 0.75

Therefore total no. of years = 5 + 0.75 = 5.75

CI = 10000 x (1 + 12%) 5.75 = 19,186.85

 

one more twist, for quarterly compounding what is the value for 71 months

one quarter has 3 months

No. of completed quarters = 23 (3 x 23 = 69)

No. of months remaining = 2 (71 – 69)

Convert months into quarterly fraction = 2/3 = 0.67

Therefore total no. of quarters = 23 + 0.67 = 23.67

CI = 10000 x (1 + 12%/4) 23.67  = 20,130.62

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