# Compound Interest Formulas and CI Practice Problems Using Shortcut Tricks

**Compound Interest: **It is the interest which is calculated not only on the principal amount invested but also on the interest earned in previous periods.

## Compound Interest Formulas

### CI Formulae:

- Amount = P[1+(r/100)]
- Compound Interest (CI) = P [ (1+r/100)
^{t}-1 ]. - Simple Interest (SI) = (CI * rt) / 100 [(1+r/100)
^{t}-1]. - When the difference between SI and CI on a certain sum for 2 years at r% is d Rs.
**Sum = (d/r**^{2})*100^{2.} ^{ }When the difference between SI and CI on a certain sum for 3 years at r% is d Rs.

**Sum = [d(100)**^{3 }/ r^{2}(300+r)].- If a sum A becomes B in t1 years at CI. Then After t2 years,
**Sum = (B)**^{t2 / t1 }/(A)(^{t2 / t1)-1}.

- The rate of Interest = [ (Difference of amount after n years and (n+1) years )/ Amount after n years ]*100.

#### Compound Interest Shortcut Trick:

While solving compound interest problems in percentage method, Always we have to assume the **principal amount (P**) is **100% **and compound interest **(CI)** is calculated based on** time** and **rate of interest.**

* For two years,* Net percentage of compound interest = CI for 1st year + CI for 2nd year.

**= ( a ) + (b + ab/100).**

*In the case of 3 years,*Then first calculate CI% for 2 years and then for the 3rd year.

**Example Problems:**

### Compound Interest Problems using Shortcut Tricks

1. Find the compound interest on Rs.5000 for two years at 5% per anum.

CI% for 2 years = a +b+ ab/100 = 5 + 5 + 25/100 = 10.25%

IF 100% = 5000

Then 10.25% = ?

By cross multiplication we get CI for 2 years =5000 * 10.25/100 =512.5

2. What will be the compound interest on Rs.5000 for 2 years at the rate of 12% p.a.?** **

**Sol:** From percentage formula Net percentage = (a+b+ab/100)%

=> [12+12+(12*12)/100]%.

= [24 +1.44]%

= > 25.44%.

We know, 100%(means principle) a 5000.

25.44% a?

e(25.44 *5000)/100 = 1272.

3. A bank offers a 5% CI on a half-year basis customer deposit 1600 Rs each on 1^{st} July of a year at the end of the year What is the interest?

**Sol:** CI = [ [2.5 + 2.5 +(2.5* 2.5)/100]+[2.5] ]*1600

4. What is the difference between CI and SI for the sum of 20000 over 2 years period? If compound interest is calculated at 20% p. a. and SI at 23% p.a.

**Sol:**_{ }R_{SI} = 23% , Net % for 2 years = 23+23 =46%.

** ** R_{CI} = 20% , Net % for 2 years = 20+20+(20*20)/100 = 44%

Difference of SI –CI = 46-44 = 2%.

If 100% à 20000 ( principle amount is always taken as 100%)

Then 2% à ?

i.e. (2 * 20000)/100 = 400.

### CI Problems Solving using Formulas

5. A sum of money invested at compound interest amounts to 800Rs. in 3 years and Rs. 882 in 5 years. What is the rate of interest?

**Sol:** [ In the case of Simple interest

[A_{m} –A_{n}] years. ]
** **But Here, In the case of Compound Interest[ A_{m} / A_{n }] years = A^{m-n }years.

- P(1+R/100)
^{5}/ P(1+R/100)^{3}= 882/800. - (1+R/100)
^{2 }years =441/400. - 1+R/100 =21/20.
- 100+ R= (21/20)*100
- R=5%.

6. On a particular amount, the CI at the end of the year is Rs. 40 and in the 2^{nd} year is 42 Rs/-.How much money was deposited?

**Sol: **Rate of interest = [(Final- Initial)/Initial] *100.

**= [(**42 **– **40)/40] *100 =(2/40)*100 = 5%.

We know, 5% à 40,

100% à?

P = (100 *40)/5 = 800.

**7.** When time T is given infraction at CI i.e. T= 3 ¾ years.

Amount = P[(1+R/100)^{3 }(1+(3/4 R)/100 )].

#### In this video, I have explained the fast calculation methods in solving compound interest problems. Once you watch this video for better understanding with examples, before going to practice the given problems below.

8. The compound interest on the certain sum of money for two years is Rs.41 and simple interest is Rs.40. What is the rate per anum?

9. The difference between the compound interest and the simple interest on a certain sum of money for two years is Rs.900. If the rate of interest is 15% per anum. What is the sum?

10. What is compound interest on Rs.50000 at the end of two years at 10% per anum?

11. A sum of money put at compound interest amounts to Rs.672 in two years and Rs.714 in three years. What is the rate of interest per anum?

12. If the difference between CI and SI on a certain sum of money @10% per anum after 3 years is Rs.6200. Find the principal amount?

13. What is the compound interest for the second year? If Rs.7500 is invested at 5% compound interest for 2 years?

Explanation: 100% = 7500

CI% for two years = 1st year + 2nd year

= a + (b + ab/100)

= 5 + (5 + 25/100)

we have to find for second year CI% = 5.25%.

IF 100% = 7500

5.25% = ?

CI for 2nd year = 5.25 *7500/100 = Rs.418.

7. What is the compound interest for the sum of Rs.8000 for 1 year at a 6% interest rate payable on Quarterly?

8. What rate percent per anum will Rs.5750 amount to Rs.6250 in two years at compound interest?

CI for two years = Amount – principal = 6250 – 5750 = Rs.500

We know 100 %(P) = 5750

?% (CI) = Rs.500

By cross multiply, 500 * 100 /5750 = 8.7%.

9. If the compound interest at the rate of 8% p.a. on a certain amount of deposit is Rs.64 more for the second year than that for the first year, What is the amount deposited?

10.If in 3 successive years, the rate interest is 5,10 and 20% per anum.What will be the Rs.1000 amount to in three years at compound interest?

For 1 st two years , 5 + 10 +50/100 = 15.5%.

For 3rd year the effective CI % = 15.5 + 20 + 310/100 = 35.5 +3.1 = 38.6%

Amount (A) = P + Interest = 100% + 38.6% = 138.%.

IF 100% (P) = 1000

Then Amount 138.6% = ?

=> 138.6* 1000/100 = Rs. 1386.