# Simple & Compound Interest Problems with Shortcuts

SIMPLE INTEREST AND COMPOUND INTEREST

The money borrowed or lent out for a certain period is called the principal or the sum.

Simple Interest

When a sum of money is borrowed for a period, an extra amount has to be paid along with the borrowed money. The fixed rate of the extra amount is called interest.

The interests are of two types : Simple Interest and Compound Interest.

Simple interest is the interest pa-id at the end of the period. Or if the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years.

Then

Compound Interest

Compound interest is interest that is paid on both the principal and also on any interest from past years. It's often used when someone reinvests any interest they gained back into the original investment. For example, if a man got 15% interest on Rs.1000 investment, the first year and he reinvested the money back into the original investment, then in the second year, he would get 15% interest on Rs.1000 and the Rs.150 he reinvested. Over time, compound interest will make much more money than simple interest.

Important Formulae :

Let Principal = P, Rate of Interest = R% and Time = T years

Important Values (Shortcut Table) :
Some more important formulae :

1. To find compound interest for two years, when simple interest is given :

Compound Interest = Total simple interest + (Simple interest for one year x Rate of Interest)

2. If the difference between the compound interest and simple interest on a certain sum of money for 2 years at R% per annum rate is Rs.'D', then

3. If the difference between the compound interest and simple interest on a certain sum of money for 2 years at R% per annum rate is Rs. 'D',

4. If the difference between the compound interest and simple interest on a certain sum of money for 3 years at R% per annum rate is Rs. 'D', then
5. If the difference between the compound interest and simple interest on a certain sum of money for 3 years at R% per annum rate is Rs.'D', then

PRACTICE QUESTIONS

1. What will be the compound interest on a sum of Rs.7200 at 5% p.a. in 2 years ?
1. Rs.841
2. Rs.738
3. Rs.793
4. Rs.812
5. Rs.694
2. What will be the compound interest on a sum of Rs.7500 at 4% per annum in 2 years ? (SBI 2012)
1. Rs.618
2. Rs.612
3. Rs.624
4. Rs.606
5. Rs.621
3. In how many years will Rs.4600 amount to Rs.5428 at 3% per annum simple interest ?
1. 3
2. 5
3. 6
4. 4
5. None of these
4. How much will a sum of Rs.7250 amount in a span of 2 years, at 6% per annum rate of compound interest? (Rounded off to the nearest integer) (SBI 2012)
1. Rs.8176
2. Rs.8146
3. Rs.8216
4. Rs.8190
5. Rs.8196
5. At what rate of simple interest will Rs.4200 amount to Rs.6216 in a span of 8 years? (SBI 2011)
1. 5
2. 3
3. 6
4. 4
5. None of these
6. At what rate of simple interest will Rs.4800 amount to Rs.6480 in a span of 7 years ?
1. 5
2. 6
3. 3
4. 4
5. None of these
7. How much will a sum of Rs.6300 amount in a span of 2 years, at 5% per annum rate of compound interest (Rounded off to the nearest interest) ?
1. Rs.6946
2. Rs.6876
3. Rs.6521
4. Rs.6790
5. Rs.6492
8. The difference between the C.I. and S.I. on a certain amount at 10% per annum for 2 years, compounded annually is Rs.372. Find the principal.
1. Rs.37,200
2. Rs.30,000
3. Rs.36,600
4. Rs.32,440
5. None of these
9. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs.l. Find the principal.
1. Rs.600
2. Rs.625
3. Rs.630
4. Rs.640
5. Rs.664
10. Find the compound interest on Rs.64,000 at 5% per annum for 18 months, compounded half yearly ?
1. Rs.2,000
2. Rs.3671
3. Rs.4231
4. Rs.4921
5. None of these
11. A man gets a simple interest of Rs.1,000 on a certain principal at the rate of 5% per annum in 4 years. What compound interest will the man get on twice the principal in two years at the same rate? (Punjab & Sind Bank PO - 2010)
1. Rs.1,000
2. Rs.1,005
3. Rs.11,025
4. Rs.10,125
5. None of these
12. The simple interest accrued on an amount of Rs.22,500 at the end of four years is Rs.10,800. What would be the compound interest accrued on the same amount at the same rate of interest at the end of two years ? (IBPS 2011)
1. Rs.16,908
2. Rs.5,724
3. Rs.28,224
4. Rs.8,586
5. None of these
Solutions :

1. Sol: P = Rs.7200, R = 5%, T = 2 years

2. Sol
P = Rs.7500, R = 4%, T = 2 years

3. Sol :

P = Rs.4600, A = Rs.5428

SI = 5428 - 4600 = Rs.828,

R = 3%,

T = ?

T = (100xSI) / PR = (100x828) / (4600 x 3) = 6 years

Ans: 3

4. Sol :

P = Rs.7250, R = 6% p.a., T = 2 years

5. Sol :

P = Rs.4200,  A = Rs.6216, T = 8 years

S.I. = A - P = 6216 - 4200 = 2016

R =  (100 x SI) / PT

= (100x2016) / (4200 x 8) = 6% pa

Ans: 3

6. Sol :

P = Rs.4800, A = Rs.6480, T = 7 years

S.I. = 6480 - 4800 = Rs.1680

R = (100 x SI) / PT

= (100 x 1680) / (4800 x 7) = 5%

Ans: 1

7. Sol :

P = Rs.6300, T = 2 years, R = 5%

8. Sol :

The sum (P) =
Ans : 1

9. Sol :

The sum (P) =

10. Sol :

P = Rs.64,000, T = 18 months

11. Sol :

12. Sol :

Ans: 2

1. 