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

## Tips , Tricks And Shortcuts on Compound Interest  and Simple Interest

Shortcuts, tips, and tricks on Compound Interest and Simple interest are not easy to find at the time of examination. So we came up with a dedicated page to help students at the crucial moment.

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 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 =$\mathbf{\frac{P × (R)^2}{(100)^2}×\frac{300+R}{100}}$
• 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

Question 2 . A lender claims to be lending at simple interest, but he adds the interest every 6 months in the calculation of principal. The rate of interest charged by him is 8%. What will be the effective rate of interest?

Options:

A. 8%

B. 8.12%

C.8.16%

D. 9%

Solution:

Let the sum be Rs. 100.

Then,

Simple interest for 1st 6 months = Rs. [100 x 8 x 1]/[100 x 2] = Rs. 4

Simple interest for last 6 months = Rs. [104 x 8 x 1]/[100 x 2] = Rs.4.16

So, amount at the end of 1 year = Rs. (100 + 4 + 4.16) = Rs. 108.16

Effective rate = (108.16 – 100) = 8.16%.

Correct option: C

Question 3 .  Rishi kapoor invested his money for a certain amount of time.The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

Options

A. Rs1800

B. Rs1750

C. Rs2000

D.  Rs1655

Solution : CI =$[4000 *((1 + \frac{10}{100})^{2})– 4000]$

=4000*$\frac{11}{10}*frac{11}{10} – 4000$

=Rs840.

Then Sum in SI = 420 (ie$\frac{840}{2}$)

=$\frac{(P*3*8)}{100}$

=Rs1750.

Correct Option : B

Question 4 . Rashmi desai took a loan of Rs. 15,000 to purchase a mobile. She promised to make the payment after three years. The company charges CI at 20% per annum for the same. But, suddenly the company announces the rate of interest as 25% per annum for the last one year of the loan period. What extra amount she has to pay due to the announcement of a new rate of interest?

Options:

A.Rs1230

B.Rs1135

C.Rs1080

D. Rs1100

Solution :
$15,000 *(1+\frac{20}{100})^{2}[ (1+\frac{25}{100}) –(1+\frac{}{100}20/100)]$

$15,000*\frac{120}{100}*\frac{120}{100}* [\frac{125}{100}-\frac{120}{100}]$

$15000*\frac{144}{100}(\frac{5}{100})$

$150*144*\frac{5}{100}=1080$

Question 5 . Abhimanyu invested his money for a certain period of time.The ratio of the amount for two years under compound interest annually and for one year under simple interest is 6:5. When the rate of interest is same, then the value of rate of interest is:

Options

A. 20%

B.15%

C.18%

D. 22%

Solution : $[P(1+\frac{r}{100})^{2}/[P(1+r*\frac{1}{100})]=\frac{6}{5}$

$1+\frac{r}{100}=\frac{}{100}$

$\frac{r}{100}=\frac{1}{5}$

r=20%

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### 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%