Answers with Explanations for Simple Interest & Compound Interest Practice Problems

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Friends, here are the answers with explanations for our Simple Interest and Compound Interest Practice Problems. Please check the practice problems from here and try to solve on your own before checking these solutions. Happy Reading.

1. Here P = Rs. 12690, T = 3 years and R = 6%

Simple Interest = PTR/100

= (12690 x 3 x 6) / 100 = Rs. 2284.20

2. Amount = P (1 +(T R/100))

Amount = 8250 ((1 + ((4x15)/100))   = Rs. 13200

Shortcut : for one year, rate of interest is 15% and for 4 years it is 15 x 4 = 60%

The amount will become 160%

If 100% money = 8250,

160% money = (160/100) x 8250 = Rs. 13200

3. C.I = P (1 + (R/100))^T-P

C.I = 9600(1 + (6/100))²-9600

= Rs. 1186.56

Shortcut : Amount = 106% of 106% of 9600 = 10786.56

So, C.I = 10786.56 - 9600 = Rs. 1186.56

4. Total Money lent to Sudeep for 4 years = 4 x Rs. 1500 = Rs. 6000

Total money lent to Raju for 2 years 

= 2 x Rs. 4500 = Rs. 9000

Total money lent = 6000 + 9000 = Rs. 15000

Interest received = Rs. 750

So, Interest % = (750 / 15000) x 100 = 5%

5. P = Rs. 12000, T =1(1/2)  . 2 = 3,  R = 4/2 = 2%

 C.I = P (1 + (R/100))^T-P

=> 12000 (1 + (2/100))³-12000

=> 12734.496 - 12000 = Rs. 734.496

6. Amount is 25000 (1 + (4/100)) (1 + 5/100))

=> So, A =  (25000 x 104 x 105) / (100 x 100) = Rs. 27300

7. Difference between Simple & Compound Interest for 2 years 

= (P x R²) / 100²

= (24000 x 49) / 10000 = Rs. 117.60

8. Interest for 2 years is Rs. 72. For one year it is Rs. 36

3% interest money is Rs. 72, then 100% money = (100 / 3) x 36 = Rs. 1200

So, Sum is Rs. 1200

9. Amount = P (1 + (TR / 100))

=> 8060 = P (1 + ((4 x 6) / 100))

=> P = (8060 x 100) / 124 = Rs. 6500

Shortcut : For one year, rate of interest is 6% and for 4 years it is 4 x 6% = 24%

Then the amount will become 124%

if 124% money is Rs. 8060, 100% money will be (100/124) x 8060 = Rs. 65000

10. Let the sum be Rs. P

So, P (1 + (R/100))³ = 6690 and P (1 + (R/100))⁶ = 10035

on dividing second by first, we get 

= (1 + (R/100))³ =10035 / 6690 = 3/2

substituting this in the first equation, 

P x (3/2) =6690 => P = Rs. 4460

11. Rest of the money is 1 - ((1/3) +(1 /6)) = 1/2

Average rate per annum on the total money

= ((1/3) x 3) + ((1/6) x 6) + ((1/2) x 8) = 6%

So, P = (100 x SI) / (T x R) = (100 x 1020) / (2 x 6) = Rs. 8500

12. Difference between Simple and Compound Interest for 3 years

=  ((300 + R) P x R²) / 100³  

=>  244 = ((300 + 5) P x 25) / 1000000

=> P = Rs. 32000

13. Let the money be Rs. X

It becomes Rs. 2 X in 3 years

As this is Compound Interest, 2 X will be the principal for next period.

Therefor, 2X will become 4X in next 3 years.

Hence Rs. X will become 4X i.e., 4 times in 3 + 3 = 6 Years

14. Amount after 5 years = 9100

Amount after 8 years = 10660

Difference = 1560, which is interest for  3 years.

Interest for 5 years = (5 / 3) x 1560 = 2600

So, Principal = 9100 - 2600 = 6500

R = (SI x 100) / (P x T) = (2600 x 100) / (6500 x 5) = 8%

15. Let the population of the town in 2009 be "X" 

=>  104% of 104% of X = 59488

=> X = 59488 x (100/104) x (100/104) = 55000

16. Total interest received for 6 years

= Rs. 5000 + 400 = Rs. 5400

Interest for one year = 5400/6 = Rs. 900

Interest % = (900/5000) x 100 = 18% p.a

17. Let the principal be Rs. X

=> ((X x 2 x 6) / 100) + ((X x 5 x 9) / 100) = ((X x 3 x 13) / 100) = 9120

=> (X / 100) (12 + 45 + 39) = 9120

=> X = Rs. 9500

Shortcut :

Let the Principal be Rs. 100

Interest for 2 years = 2 x 6 = 12

Interest for 5 years = 5 x 9 = 45

Interest for 3 years = 3 x 13 = 39

Total interest = 12 + 45 + 39 = Rs. 96

If the total interest is Rs.9120, then the Principal = (9120 / 96) x 100 = Rs. 9500

18. R = (100 x SI) / (P x T) 

=> R = (100 x 252) / (1400 x 3) = 6%

Now the rate of Interest = 6 + 3 = 9%

=> New Amount = P (1 + (TR/100))

= 1400 ( 1 + ((3 x 9) / 100)) = Rs. 1778. 

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