单利按贷款本金或原始金额计算。如果原理= p，利率= r，时间= t，则SI =(p * t * r)/ 100 。但是，复利是根据本金以及前期的累计利息来计算的。它也被称为“兴趣上的利息”。
- 每年复利时，金额A = P(1 + R / 100) n
- 当半年复利时，金额A = P {1 +(R / 2)/ 100} 2n
[半年一次：每年计算两次，因此rate(R)除以2，年数(n)乘以2]
Now Compound interest (C.I) = Amount – Principle
C.I = P[(1 + r/100)n – 1]
一些要点和有用的公式
最终金额
将一定时期末的利息添加到原始总和(P)中，以得到该金额。现在，此金额成为下一个期间的原则。重复此过程，直到找到最后一个期间的金额，即最终金额(A)。
连续年的复利
如果我们有相同的金额和相同的利率。特定年份的CI总是大于上一年的CI。 (第三年的CI大于第二年的CI)。连续两年的CI之间的差额为上一年CI的一年利息。
C.I of 3rd year – C.I of 2nd year = C.I of 2nd year * r * 1/100
[r = rate; t = 1 year]
连续两年的金额之间的差额是前一年金额的一年利息。
Amount of 3rd year – Amount of 2nd year = Amount of 2nd year * r * 1/100
[r = rate; t = 1 year]
关键结果
当我们有相同的金额和相同的费率时，
C.I for nth year = C.I for (n – 1)th year + Interest for one year on C.I for (n – 1)th year.
C.I for 6th year = C.I for 5th year + Interest for one year on C.I for 5th year
对于金额，
The amount for 6th year = Amount for 5th year + Interest for one year on Amount for 5th year.
金额的其他一些应用
增长：主要用于与行业相关的增长。
Production after n years = initial production * (1 + r/100)n
折旧：当某产品的成本每年贬值r％时，则n年后的价值为
Present value * (1 + r/100)n
人口问题：当一个城镇，城市，村庄的人口每年以一定速度增长时。
Population after n years = present population * (1 + r/100)n
例子
例1：当本金= 6000卢比，利率=每年10％，时间= 2年时，找到复利?
解决方案：
Interest for first year = (6000 * 10 * 1)/100 = 600
Amount at the end of first year = 6000 + 600 = 6600
Principal interest for second year = (6600 * 10 * 1) / 100 = 660
Amount at the end of second year = 6600 + 660 = 7260
Compound Interest = 7260 – 6000 = 1260
示例2：当年利率为2％时，两年内8000卢比的复利是多少?
解决方案：
Given principal P = 8000
rate r = 2%
time = 2years
by formula ,
A = P (1 + R/100)n
= 8000 (1 + 2/100)2
= 8000 (102/100)2
= 8323
Compound interest = A – P
= 8323 – 8000
= Rs 323
例3：Hari存入卢比。 4000美元，在一家金融公司工作了2年，年利率为5％。 Rohit两年后可获得的复利是多少?
解决方案：
Given
pricipal P = 4000
rate r = 5%
time = 2years
By formula ,
A = P (1 + R/100)n
= 4000 (1 + 5/100)2
= 4000 (105/100)2
= 4410
Compound Interest = A – P
= 4410 – 4000
= 410
例4：找到Rs的复利。 2000年，年利率为4年，为期1.5年。每半年复利一次?
解决方案：
Given,
principal p = 2000
rate r = 4%
time = 1.5 ( i.e 3 half years )
by formula ,
A = P (1 + R/200)2n
= 2000 (1 + 4/200)3
= 2000 (204/200)3
= 2122
Compound Interest = A – P
= 2122 – 2000
= 122
示例5：如果按季度复利，则10000的一年期复利是多少，年利率为20％?
解决方案：
Given,
Principal P = Rs 10000
rate R = 12% (12/4 = 3 % per quarter year)
Time = 1 year (1 * 4 = 4 quarters)
by formula,
A = P (1 + R/100)n
= 10000 (1 + 3/100)4
= 10000 (103/100)4
= 11255
Compound Interest = A – P
= 11255 – 10000
= 1255
例6：在该本金上，以2年每年5％的利率计算复利，给定Rs，在2年内以每年5％的利率计算。像400简单的兴趣?
解决方案：
Given
Simple interest SI = 400
rate R = 5%
time T = 2years
by formula,
Simple interest = (P * T * R)/100
P = (SI * 100)/T * R
= (400 * 100)/2 * 5
= 40000/10
= Rs 4000
Rate of Compound Interest = 5%
time = 2 years
by formula ,
A = P (1 + R/100)
= 4000 (1 + 5/100)
= 4410
Compound Interest = A – P
= 4410 – 4000
= 410