A man has $100 and decides to invest it in a bank for 6 years. The bank gives him two choices, annual rate of interest 2%, compounded annually,...

Since the bank is paying compound interest , we have to use the formula for compound interest for calculating the amount.

The formula is,

`A_t=P(1+r/n)^(nt)`  

where ,

`A_t`  is the amount at the end of t years of investment

P is the principal

r is the annual rate of interest, 

n is the number of compounding periods per year

Case 1

Given P=$100, t= 6 years , n=1 as interest is compounded annually, r=2%

Now plug in the given values in the formula to calculate the amount at the end of 6 years of investment,

So, `A_6=100(1+2/100)^6`

`A_6=100(1+1/50)^6`

`=100(51/50)^6`

`=100(1.02)^6`

`=112.6162419`

`~~112.62`

Case 2 

Given: P=$100 , r=1.8% , n=4 ( as interest is compounded quarterly ) , t=6 years

Now plug the given values in the formula to calculate the amount at the end of 6 years,

`A_6=100(1+1.8/(4*100))^(4*6)`

`=100(1.0045)^24`

`=111.3777874`

`~~111.38`

So the first option is better with annual rate of interest 2% compounded annually, as the amount received after 6 years of investment is more than the second option.