Question

Rs. 2,500 invested at a certain rate for a certain even number of years, compounded annually, grows to Rs. 2,809 . How much amount it would grow if it is invested at the same rate for half the period at simple interest?

1. Rs. 2,650
2. Rs. 2,800
3. Rs. 3,000
4. Rs. 2,700

Answer 1

Correct Answer - Option 1 : Rs. 2,650

Given:

Amount is Rs. 2,809

Principal is Rs. 2,500

Formula Used:

A = P(1 + R/100)n,

CI = A – P,

where, 

A is amount, 

P is principle,

R is rate of interest, 

n is total number of years,

And for Simple Interest,

SI = (P × N × R)/100,

Where,

P is principle,

SI is simple interest,

N is total number of years,

R is rate

Calculations:

Amount = P (1 + R/100)ⁿ

⇒ 2,809 = 2,500 (1 + R/100)²ⁿ

⇒ 2,809/2,500 = (1 + R/100)²

⇒ 53/50 = (1 + R/100)

⇒ R = 6%

Now using formula for Simple Interest,

⇒ SI = (2,500 × 6 × 1)/100

⇒ 150

Amount = P + SI

⇒ 2,500 + 150

⇒ Rs. 2,650

∴ The amount it would grow is Rs. 2,650.