What is Compound Interest

Inter­est cal­cu­lat­ed on the ini­tial prin­ci­pal and also on the accu­mu­lat­ed inter­est of pre­vi­ous peri­ods of a deposit or loan. Com­pound inter­est can be thought of as “inter­est on inter­est,” and will make a deposit or loan grow at a faster rate than sim­ple inter­est, which is inter­est cal­cu­lat­ed only on the prin­ci­pal amount. The rate at which com­pound inter­est accrues depends on the fre­quen­cy of com­pound­ing; the high­er the num­ber of com­pound­ing peri­ods, the greater the com­pound inter­est. Thus, the amount of com­pound inter­est accrued on Rs.1,00,000 com­pound­ed at 10% annu­al­ly will be low­er than that on Rs. 1,00,000 com­pound­ed at 5% semi-annu­al­ly over the same time peri­od. Com­pound inter­est is also known as compounding.

For­mu­la

The for­mu­la for cal­cu­lat­ing com­pound inter­est is:

Com­pound Inter­est = Total amount of Prin­ci­pal and Inter­est in future (or Future Val­ue) less Prin­ci­pal amount at present (or Present Value)

                                = [P (1 + i)ⁿ] – P

                                = P [(1 + i)ⁿ – 1]

(Where P = Prin­ci­pal, i = nom­i­nal annu­al inter­est rate in per­cent­age terms, and n = num­ber of com­pound­ing periods.)

If the num­ber of com­pound­ing peri­ods is more than once a year, “i” and “n” must be adjust­ed accord­ing­ly. The “i” must be divid­ed by the num­ber of com­pound­ing peri­ods per year, and “n” is the num­ber of com­pound­ing peri­ods per year times the loan or deposit’s matu­ri­ty peri­od in years.

For exam­ple:

• The com­pound inter­est on Rs.10,000 com­pound­ed annu­al­ly at 10% (i = 10%) for 10 years (n = 10) would be = Rs.25,937.42 — Rs.10,000 = Rs.15,937.42
• The amount of com­pound inter­est on Rs.10,000 com­pound­ed semi-annu­al­ly at 5% (i = 5%) for 10 years (n = 20) would be = Rs.26,532.98 — Rs.10,000 = Rs.16,532.98
• The amount of com­pound inter­est on Rs.10,000 com­pound­ed month­ly at 10% (i = 0.833%) for 10 years (n = 120) would be = Rs.27,070.41 — Rs.10,000 = Rs.17,070.41

Com­pound inter­est can sig­nif­i­cant­ly boost invest­ment returns over the long term. While a Rs.1,00,000 deposit that receives 5% sim­ple inter­est would earn Rs.50,000 in inter­est over 10 years, com­pound inter­est of 5% on Rs.1,00,000 would amount to Rs.62,889.46 over the same period.