Question

A man invests a sum of money at 5% per annum for two years compounded half yearly and gets
a bonus of 1% at the end of 2 years. He invests a similar amount at 6% compounded annually for
2 vears. Which is a better investment?​

Answer 1

Given :

The rate of interest = 5 % compounded half yearly

The time period for investment = t = 2 years

The bonus amount = 1% at end of 2 years

Again

At 6 % compounded annual , for 2 years, Similar amount investment

To Find :

The better investment plan

Solution :

Let The principal investment at both rate = Rs p

From Compound interest semi annual

Amount = principal × $(1+\dfrac{rate}{2\times 100})^{2\times time}$

             = p × $(1+\dfrac{5}{2\times 100})^{2\times 2}$

             = p × $(1.025)^{4}$

             = p × 1.1038

∵  After 2 years, 1% bonus

i,.e  Interest = 1% of investment

                    = 0.01 p

∵  Amount = Principal + Interest

Or,   p × 1.1038 = p + 0.01 p

Again

At Compound interest annual

Amount = principal × $(1+\dfrac{rate}{ 100})^{time}$

             = p × $(1+\dfrac{6}{ 100})^{ 2}$

             = p × $(1.06)^{2}$

             = p × 1.123

∵  Amount at 6% compound annual = 1.123 p

And Amount at 5% compound semi-annual = 1.103 p

Hence, The better investment plan is at 6% compounded annual Answer