Question

Piyush invests Rs. 30,000 at 5% per annum for 2 years at simple interest. After completing 2 years He also invests all the amount at 10% per annum for 3 years on compound interest. Then find the total interest gain by Piyush. 
1. Rs. 9,953
2. Rs. 13,923 
3. Rs. 10,923
4. Rs. 12,433

Answer 1

Correct Answer - Option 2 : Rs. 13,923 

Given:

Money invest on simple interest = Rs. 30,000

Rate for simple interest = 5% 

Time for simple interest = 2 years 

Rate for compound interest = 10% 

Time for compound interest = 3 years 

Concept used:

S.I. = (P × R × T)/100 

A = P + S.I.

C.I = P × (1 + R/100)^T – P 

Where,

S.I → Simple interest

A → Amount 

C.I → Compound interest 

P → Principal 

R → Rate 

T → Time 

Calculations:

S.I = (30,000 × 5 × 2)/100 = Rs. 3,000

Amount = 30,000 + 3,000 = 33,000

Principal for C.I = Rs. 33000

C.I = 33,000 × (1 + 10/100)³ – 33,000

⇒ 33,000 × (110/100)³ – 33,000

⇒ 33,000 × (11/10) × (11/10) × (11/10) – 33,000

⇒ 43,923 – 33,000 = Rs. 10,923 

Total interest = Rs. 3000 + Rs. 10,923 = Rs. 13,923

∴ Total interest gain by Piyush is Rs. 13,923