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# Simple Interest and Compound Interest Practice Problems with Easy Tricks

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# Simple Interest and Compound Interest Practice Problems with Easy Tricks:

To solve SI and CI problems we have different methods as using formulas, shortcut methods and tricks but we have to apply appropriate method which is required to get answer in less time. At some places we get quick answer by applying direct formula and at some places shortcut methods.
SI & CI Formulas:
Principal Amount – (P), Time – (T), Rate of Interest (R), Simple Interest (SI).

SI = (PTR) / 100.
CI = p[(1+R/100)^t – 1].

## Compound Interest Shortcuts:

• 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 the certain sum for 2 years at r% is d Rs.  Sum = (d/r2 )*1002.
•  When the difference between SI and CI on a certain sum for 3 years at r% is d Rs. Sum = [d(100)3 / r2(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.

1. In how many years simple interest be equal to the principle amount at 25% p.a. interest rate?

SI of n years = P
=> P T R /100 = P
=> T = 100/R = 100/25 = 4 years.

2. The simple interest on certain principle amount P at 7% per anum for 4 years is 3584. What will be compound inerest on same principle for 2 years at 4% per anum?

Explaination: Here we have to use shortcut method than applying formula.
Shortcut method: if we have rate of interest (r%) and time period in years (1,2,3…n years)
SI for 2 years = (r% + r%) of P

CI for 2 years = [r% +r% + (r*r)/100] of P.
SI for 4 years = 1st year + 2nd year + 3rd year + 4th year.
= 7 + 7 + 7 + 7 = 28%.

Here, 28% = 3584
Then 100% = P
Therefore P = (100 * 3584)/28 = 100 * 512/4 = 100 * 128 = 12800.

CI of 2 years at 4% rate.
= 4 + 4 + 16/100 = 8+0.16 = 8.16%

we have from question that 28% = 3584.
Then 8.16% = ?

=> (8.16 * 3584)/28 = 128 * 8.16 = 1044.48.
3. Akshaya received Rs.5175 as simple interest on the amount of Rs.15000 fixed for 2 years. Find out the rate of simple interest.
Explaination: Here we have to use the direct formula SI = PTR/100 i.e. R= (SI * 100 )/ PT. Answer is 17.25%.
4. The principle amount becomes 5 times of itself in 10 years. What should be the rate of interest per anum?

Assume p = 100 and it becomes 5 times means 500. Then the interest is 400 i.e. 4P.

PTR/100 = 4P
=> P*10*R/100 = 4P,
=> R = 40%.
5. What would be the simple interest obtained on an amount of Rs.8930 at the rate of 8% per anum after 5 years?

Always principle amount (P) be 100%. SI for 5 years = 5 * 8 = 40%.
Here 100% = 8930.
=> 40% =?

=> (40 * 8930)/100 = 3572.

6. What would be the compound interest (CI) obtained on an amount of Rs.4000 at the rate of 5% per anum after 3 years?

P= 100%, CI for 3 years = 1st calculate for 2years

for 2 years = 5 + 5 + 25/100 = 10.25
then for 3rd year = 10.25 + 5 + 0.52 = 15.77
100% = 4000
15.77% = ? => 15.77 * 4000/100 = 631.

7. What will be the simple interest accrued on a sum of Rs.5224 at a rate of 5% per anum in 6 years?

Always Principle amount (P) = 100% and SI for 6 years = 6*5 =30%.

100% = 5224
30% = ?
=> (30 * 5224)/100 = 1306.

(If we learn this percentage based solving trick we can get answer in less than 10 seconds.)
8. What will be the amount of compound interest (CI) accrued on an amount of Rs.16,400 at the rate of 8% in two years?

P = Rs.16,400. CI rate for 2 years = 8 + 8 + (8*8)/100 = 16 + 0.64 = 16.64%.

100% = 16,400
16.64% = ?

=> (16400 * 16.64)/100 = 164 * 16.64 = 2729.
9. The compound interest on a certain amount for 2 years at the rate of 8% is Rs.312. What will be the simple interest on the same amount and at the same interest rate and same time?

Here P= 100% = Rs.x and CI for 2 years = 8 + 8 + (8*8)/100 = 16.64% = Rs.312(given)

Then, 16.64% = 312
100% = ? (Find P)

=> P= 312 * 100 /16.64 = 1875.

We have to find SI for 2 years at 8% Rate on 1875.
=> 100% = 1875
16% = ?

=> SI for 2 years = (16* 1875)/100 = 300.

10. What will be the total amount will ramya get in 2 years if she invests Rs.5000 to obtain compound interest at 5% per anum rate?
Here Principle P = 100%, CI for 2 years = 5 + 5 + 25/100 = 10.25% Then Total Amount = Principle +Interest = 100% + 10.25% = 110.25%

We have 100% = 5000
110.25% = ? (Total amount)

Total amount = (110.25 * 5000)/100 = Rs.5512.50

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