# Tips Tricks And Shortcuts on Compound Interest And Simple Interest Problems

## Tips , Tricks And Shortcuts on Compound Interest (CI) and Simple Interest (SI)

**Simple interest is based on the principal amount of a sum of money. While the compound interest is based on the principal amount and the previous accumulated interest.**

### Tips and Tricks to Crack CI and SI Problems

- Compound Interest is always calculated on the Amount (Principal + Interest) .

- Simple interest is always calculated on Principal .

- If a sum of money P amounts to A
_{1}in n time at SI and the same sum of money amounts to A_{2}in n time at CI, it can be calculate as\mathbf{\frac{P}{A_{1}} =\frac{A}{A_{2}} }

- A sum at a rate of interest compounded yearly becomes Rs. A
_{1}in n years and Rs. A_{2}in (t + 1) years, then P =\mathbf{A_{1}(\frac{A_{1}}{A_{2}})^t} .

- Difference between CI and SI for 2 years = \mathbf{\frac{P × (R)^2}{(100)^2}}

- Difference between CI and SI for 3 years =\mathbf{\frac{P × (R)^2}{(100)^2}×\frac{P × (R)^3}{(100)^3}}

- If a sum A becomes B in t
_{1}years at CI. Then After t_{2}years, Sum = \mathbf{\frac{(B)^\frac{t_{2}}{t_{1}}}{(A)^\frac{t_{2}}{t_{1}}-1}}

**Type 1: Simple and Compound Interest Tips and Tricks and Shortcuts. Solve Difference between CI and SI**

**Question 1. Find out the difference between Compound Interest and Simple interest for the sum of 10000 over 2 years period. If CI and SI is calculated at 20% and 23% p.a. respectively.**

**Options: **

**A. 200**

**B. 400**

**C. 100**

**D. 2000**

**Solution: **R_{SI }for 2 years = 23 + 23 = 46%

R_{CI} for two years = 20 + 20 + \frac{20×20}{100} = 44%

Difference between CI and SI = 46 – 42 = 4%

Let the principal amount = 100%

Then 4% will be

\frac{4×10000}{100}

\frac{40000}{100} = 400

**Correct option: B**

**Type 2: Find the amount/time/rate of interest when CI or SI or their difference is given.**

**Question 2. The difference between the compound and simple interest on a certain sum at 12% p.a. for 2 years is Rs. 90. What will be the value of the amount at the end of 3 years if compounded annually?**

**Options:**

**A. Rs. 8890.80**

**B. Rs. 8870.80**

**C. Rs. 8780.80**

**D. Rs. 8780**

**Solution: **Difference between CI and SI = \frac{P × (r)^2}{(100)^2}

90 = \frac{P × (12)^2}{(100)^2}

P = \frac{90 × (100)^2}{(12)^2}

P = \frac{90 × 10000}{144}

P = 6250

Now, calculate the compound interest on Rs. 6250

A = 6250(1+ \frac{12}{100})^{3}

A = Rs. 8780.80

**Correct option: C**

**Read Also – ****How to solve Compound Interest and Simple Interest Problem**

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RSI for 2 years = 23 + 23 = 46%

RCI for two years = 20 + 20 + (20*20)/100 = 44%

Difference between CI and SI = 46 – 42 = 4%//wrong

as 46-44=2%