Question

Which is better investment 8% compounded half-yearly or 7.9% compounded

monthly?​

Answer 1

Given:

Investment 7.9% compounded monthly and 8% compounded half-yearly.

To find:

Better investment.

Solution:

To differentiate find the amount received after a fixed time interval.

1) The amount received after the six months in the investment of 7.9% compounded monthly is given by:

• Amt = P (1  + 7.9/1200)⁶

•        = 1.0401P  

2) And the amount received after the six months in the second case that is an investment at 8% compounded half-yearly is given by:

• Amt = P (1 + 4/100)  

•       =  1.04P

So the amount received in investment at the rate of 7.9% is slightly more.

Investment at 7.9% is quite better

Answer 2

Given :   investment 8% compounded half-yearly or 7.9% compounded

monthly  

To find : Which is better investment

Solution:

Let say Investment  = P

A = P(1 + R/100)ⁿ

More the Amount for Same amount & same period , better the investment

8 % is Compounded Half  yearly  

=> 4 % interest rate for 6  month

Amount after 6 months would be

P (1 + 4/100)  =  1.04P

7.9% compounded  monthly

=> Monthly interest rate = (7.9/12) %

Amount after 6 months would be

= P (1  + 7.9/1200)⁶

= 1.0401P  

1.04015P    is Slightly more than 1.04P

Hence 7.9% compounded   monthly is Slightly better  than 8% compounded half-yearly  

But Difference is very less so we can even Say that both are almost equivalent  

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