Question

Given an investment of Rs. 10000 for a period of one year, it is better to invest in a scheme that pays: 

Options
 12% interest compounded annually

 12% interest compounded quarterly

 12% interest compounded monthly

 12% interest compounded daily

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Answer 1

Answer:

12% interest compounded daily

Answer 2

Option(4) 12% interest compounded daily is the correct answer.

Given,

Initial investment(P) = Rs. 10000

Time(t) = 1 year

To Find,

Best scheme to invest =?

Solution,

From the formula of compound interest, we have

$A = P ( 1 + r / n)^{nt}$

Case 1:  12% interest compounded annually. That means, r = 12% and n = 1

$A = 10000 ( 1 + \frac{12}{100*1} )^{1*1}\\A = 10000 ( 1 + 0.12} )^1\\A = 10000(1.12)\\A = 11,200$

The final amount after 1 year will be Rs. 11,200.

Case 2:  12% interest compounded quarterly. That means, r = 12% and n=4

$A = 10000 ( 1 + \frac{12}{100*4} )^{4*1}\\A = 10000 ( 1 + 0.03} )^4\\A = 10000(1.125)\\A = 11,255.1$

The final amount after 1 year will be Rs. 11,255

Case 3:  12% interest compounded monthly. That means, r = 12% and n=12

$A = 10000 ( 1 + \frac{12}{100*12} )^{12*1}\\A = 10000 ( 1 + 0.01} )^{12}\\A = 10000(1.126)\\A = 11,268.25$

The final amount after 1 year will be Rs. 11,268

Case 4:  12% interest compounded daily. That means, r = 12% and n=365

$A = 10000 ( 1 + \frac{12}{100*365} )^{365*1}\\A = 10000 ( 1 + 0.0033} )^365\\A = 10000(1.127)\\A = 11,274.75$

The final amount after 1 year will be Rs. 11,275

The final amount is maximum in case 4 i.e. Rs. 11,275.

Hence, it is better to invest in a scheme that pays 12% interest compounded daily.