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

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

### 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 A1 in n time at SI and the same sum of money amounts to A2 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. A1in n years and Rs. A2 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 t1 years at CI. Then After t2 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:     RSI for 2 years = 23 + 23 = 46%

RCI for two years = 20 + 20 + $\frac{20×20}{100}$ = 44%

Difference between CI and SI = 46 – 44 = 2%

Let the principal amount = 100%

Then 2% will be

$\frac{2×10000}{100}$

$\frac{20000}{100}$ = 200

Correct option: A

### 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

### One comment on “Tips Tricks And Shortcuts on Compound Interest And Simple Interest Problems”

• Chandra

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%