Compound Interest Solved Problems

Introduction

Solve problems regarding compound interest with Nithra Jobs help. To succeed in competitive exams, continue to routinely practise compound interest questions with solutions using the compound interest formula.

Formulas to use:

Interest is Compounded Annually

Amount = P (1+ (r/100)) ^{n

Compound Interest = Total amount - Principal

Interest is Compounded Half-Yearly

Amount = P (1 + ((r/2) / 100)) ²ⁿ

Compound Interest = Total amount - Principal

Interest is Compounded Quarterly

Amount = P (1 + ((r/4) / 100)) ⁴ⁿ

Compound Interest = Total amount - Principal

Interest is Compound Monthly

Amount = P (1 + (r / 12 / 100) ¹²ⁿ

Interest is Compounded Annually but Time is in Fraction, say 2(3/2) years Amount = P (1 + r/100) ² × (1 + (3/2)r/100)

CI when Rates are Different for Different Years Amount = P (1 + r1/100) (1 + r2/100) (1 + r3/100)}

6. The Simple interest on a certain sum for 2 years at 10% per annum is Rs. 150. The corresponding compound interest is?

Answer: Rs. 1575

Explanation:

Given data, Time = 2 years Rate = 10 %

Simple interest = Rs. 150

Formula, Principal = ( Simple interest × 100 ) / N × R Principal = ( 150 × 100 ) / ( 2 × 10 )

= 150000 / 20

= Rs. 7500

Formula, Compound Interest = [ Principal × { 1 + ( R / 100 ) }ⁿ - Principal ]

= 7500 × [ 1 + ( 10 / 100 ) ]² - 7500

= [ 7500 × ( 11 / 10 ) × ( 11 / 10 ) ] - 7500

= 9075 - 7500

= Rs. 1575

The corresponding compound interest is Rs. 1575.

7. If the difference between the simple interest and compound interests on some principal amount at 20 % for 3 years is Rs. 45, then the principal amount is?

Answer: Rs. 351.5625

Explanation:

Formula, Principal = [ ( Difference × 1003 ) ] / [ r² ( 300 + Rate ) ] Let P be Sum and R be rate of interest

R = 10 %

Difference between S.I and C.I is Rs. 45

P = [ ( 45 × 100 × 100 × 100 ) ] / [ 20 × 20 ( 300 + 20 ) ]

= Rs. 351.5625

The principal amount is Rs. 351.5625.

8. Riyaz deposited an amount of Rs.6000 for 3 years at 12% per annum. If he deposited this much of amount in compound interest, then what?s the total amount of money he got after 3 years?

Answer: Rs. 8429.568

Explanation:

Given, Principal (P) = Rs.6000 Rate (R) = 12 %

Time (n) = 3 Years

Formula, Amount = P [ 1 + (R/100 ) ]ⁿ

= 6000 [ 1+ ( 12 / 100 ) ]³

= 6000 × [ ( 100 + 12 ) / 100 ]³

= 6000 × [112 / 100 ]³

= 6000 × 1404928 / 1000000

= 8429.568

Amount = Rs. 8429.568

9. What sum invested for 2 years at 10 % compounded annually will grow to Rs. 5808?

Answer: Rs. 4800

Explanation:

Formula,

Amount = P [ 1 + ( R / 100 ) ]ⁿ Here, Amount = Rs. 5808

N = 2

R = 10 %

5808 = P [ 1 + ( 10 / 100 ) ]²

5808 = P [ 11 / 10 ]²

P = 5808 × 10 × 10 / ( 11 × 11 )

= Rs. 4800

The sum invested is Rs. 4800.

10. A sum of money is borrowed and paid back in two annual installments of Rs. 1120 each allowing 5% compound interest. The sum borrowed was?

Answer: Rs. 2416.54

Explanation:

Formula,

The sum borrowed = Sum for instalments + Sum for instalments × [ 1 + ( r / 100 ) ] × [ 1 + ( r / 100 ) ]²

Here, r = 5 %

Sum for instalments = Rs. 1120

The sum borrowed = 1120 + 1120 × [ 1 + ( 5 / 100 ) ] × [ 1 + ( 5 / 100 ) ]²

= 1120 + 1120 × ( 21 / 20 ) × ( 21 / 20 ) × ( 21 / 20 )

= 1120 + 1296.

= Rs. 2416.54

The sum borrowed is Rs. 2416.54.

Conclusion

Some of the candidates are unclear about compound interes formulas. We have provided the compound interest questions for competitive exams, along with solutions and formulas. Nithra Jobs is helpful for the job seekers in learning quickly and simply.