Today I am going to share Simple Interest and Compound Interest tricks and shortcuts.
Simple Interest
Formula of Simple Interest:
Examples
#1
Find the simple interest, If
- P = Rs.1000, R = 20% per annum, T = 4 years.
- P = Rs.600, R = 5% per annum, T = 4 months.
- P = Rs.200, R = 6% per six months, T = 3 years.
- P = Rs.500, R = 2% per six months, T = 5/2 years.
- P = Rs.400, R = 3% per three months, T = 2 months.
- P = Rs.730, R = 10% per annum, T = 120 days.
- P = Rs. 3000, R = 61/4 per annum, T = period from 4th Feb to 18th Apr.
# Solution
- 4×20×10 ⇒ 800
- 2×5 = 10
- 6×2×3×2 = 72
- 5×2×5=50
- 4×2=8
- 73/3=24
- 37.50
![Tricks to find Simple Interest Trick to find simple interest](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCq_yxsJBbHDSzDiwYmoAykU5SIqQi4OQdNDWgj2rvp41QqfiLU-YHWJqG7dkf2F0N9vdQUbFbBUXul_MgbqA01fRBaVIatdLeEV7br_Ml0HL1G5oObN5UBBelljIDgKZlL5qtq__o_lPk/s400-rw/imageedit_8_8050957225.jpg)
#2
Find the following:
- P = Rs. 100, R = 3% per annum, T = 2 year, A= ?
- P = Rs. 500, R = 6% per annum, T = 4 months, A= ?
- P = Rs. 400, R = 3.65% per annum, T = 150 days, A= ?
- A = Rs. 540, S.I = Rs. 108 , R = 5%, T = ?
- A = Rs. 1,120, R = 5%, T = 22/5 yr, S.I = ?
# Solution:
- S.I = 6 ; A = S.I + principal ; A = 6 + 100 ⇒ 106
- S.I = 10 ; A = S.I + P ; A = 10+500 ⇒ 510
- S.I = 6 ; A = 400 + 6 ⇒ 406
- T = 5 yr.
- 120
#3
- A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. Find the sum and the rate %.
- Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of Rs. 11,400 at the end of nine years , how much money did he borrow ?(Bank P.O 1999)
- A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 61/4% p.a. for 2 years. Find his gain in the transaction per year.(S.S.C.2000)
- A certain sum of money amounts to Rs. 1008 in 2 years and to Rs. 1164 in 31/2 years.Find the sum and the rate of interest?
- The simple interest on a certain sum of money for 21/2 years at 12% per annum is Rs. 40 less than the simple interest on the same sum for 31/2 years at 10% per annum. Find the sum.
# Solution
- Principal = 600, R = 10%
- 12000
- 112.50
- [ 1164-1008 = 156 ] ⇒ 156/3×4 = 208 ; R = 208/2×800×100 ⇒ 13
- 7x/20 - 3x/10 = 40 ⇒ x = ( 40 × 20 ) ⇒ x = 800 [ Hint : Given Below ]
Compound Interest
Formula of Compound Interest:
Trick :
Calculating Compound Interest for 3 Years
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Calculating Compound Interest for 4 year
![Trick for Compound Interest Trick for CI](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEUyVJplTR_ymDb0gUeSHgi7sno1-lYhyphenhyphenc_5aAiiRHwV9Zmm-IrqC_8XywItqLpK1eywOOAYLx2V9l-Y_u74khbxVUZXe1Q6HyVARY53qnhU3w2StJc9aXS-sNB2U6SjVUNitieEcl0fMM/s320-rw/Compound+interest+for+4+year.png)
# Formulas
![formulas for compound interest how to calculate compounding interest](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg01GJlFa2PPnmRjqwYIHIqCzrOmEfKXd9GpcsA9s8-G-No7pZVbneWYmf2wL0NVqykV45YkhVbcaFlXiKfaqPYAMRn0JgE9z0QqWc_Ku2qm49v2ip-O9UCLKmBE4kzeNBb2BttmSxrllRR/s320-rw/Basic+Formulas.gif)
Case 1. When interest is not Compound yearly,
Amount after 't' years A = P [1+ r/n×100]nt
n= no of compounding per year
When interest is compounded half yearly, n = 2
compounded quarterly, n = 4
compounded monthly, n = 12
Case 2. When rate % is no equal every year and interest is compounded yearly
Basic formula :
P [1+ r/100] [1+ r/100] ...upto 't' times
But as rate % is not same every year, so
A = P [1+ r1/100]t1 [1+ r2/100]t2 .... and so on
Where R1 = Rate% p.a. for t1 years. and R2 = Rate % p.a. for t2 years.
Case 3 When interest is compounded yearly but time is in fraction
T = 53/4 years
A= (whole part) × (fraction part of time )
A = P [1+ r/100]5 × [1+ 3r/4/100]
P [1+ r/100] [1+ r/100] ...upto 't' times
But as rate % is not same every year, so
A = P [1+ r1/100]t1 [1+ r2/100]t2 .... and so on
Where R1 = Rate% p.a. for t1 years. and R2 = Rate % p.a. for t2 years.
Case 3 When interest is compounded yearly but time is in fraction
T = 53/4 years
A= (whole part) × (fraction part of time )
A = P [1+ r/100]5 × [1+ 3r/4/100]
# Difference between Compound Interest and Simple Interest
CI - SI = P [ R/100 ]2
When time t = 3 years
CI - SI = P [ (R/1003 +3 (R/100)2]
# Examples
#1
- If the compound interest on a certain sum for two years at 10% p.a. is Rs 2,100 the simple interest on it at the same rate for two years will be. ( RRB, 2009)
- The compound interest on a sum for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound and simple interest for 3 years will be.
- The difference between simple interest and compound interest on a sum for 2 years at 8% when the interest is compounded annually is Rs. 16, if the interest were compounded half yearly, the difference in one interest would be nearly.
- The difference in C.I and S.I for 2 years on a sum of money is Rs. 160.If the S.I for 2 years be Rs. 2880, the rate of percent is .
# Solution
1. 2000
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2. 98.56
![compound interest questions for bank exams compound interest questions and solutions](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTQWj6cFUyEiQPNL2Ub1V6Dva2Uxv1P2u3pmq6qrOYc8N1s0SzOiuAbMb5HpjcEymdYGXejCXuIt9rR_nskniLg076J1Q_iiYkNyvWcEVegho3gc0HyNmeaZPZJ1iTHTl0ZvMLwYeeT1zn/s320-rw/imageedit__3742172755.gif)
3. 04
![compound interest questions worksheet compound interest formula and examples](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl7akI_Obj7qLH3a73oUrYT-K7XwOCHMWfSxYPxmA9O1hbVNl6siAhkJai0mkvILIU-rAIdm0ITotBk7pVu9BHmq9jA4kH1hxHM2wvh6iCZ63IA-C2ykca4SWWdlMa7ROuQxkxnLPXNVf5/s1600-rw/imageedit_4_7058985836.gif)
![compound interest formula compound interest examples](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOSzmIL926Pve5HTcs4F2IZ5kjdOA3REmseS0UyZi7TQKQE8ea3M1dFF1B58xarpl1FbFeBmd2EpnFKisNp452YHAy9VFbrLhlqnM4qU-bN29XHB-NKfIeGos6yvLj6nYNrFKDyZWeHC86/s400-rw/imageedit_7_6587088774.gif)
4.
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