1 part $5000 at 6.6% interest monthly for 6years. 2nd part $1100 at 4.8% compounded annually for 6 years.

The first part:

Principle , P =$5000  is invested for 6 years at the  rate of 6.6% .The interest is on  a monthly basis.You did not say whether it is compoundibg or simple interest. So, the monthly rate of interest is 6.6%= 6.6/12  %=0.55% = 0.0055 per dollar.

The amount after 6 years = P+P*nr, where P = principle, n number of months =6*12 = 72 and r is the rate of monthly interest per dollar. So, the amount including the simple interest for 72 months is given by:

Principle +interest on the principle = 5000+5000*72*0.0055=$(5000+1980) = $6980  including the simple interest. It is as good as the simple interest for 6 years.

The second part:

The investment is in compound interest annually. Pinciple ,P = $1100. The annual rate  of interest = 4.8%. Therefore, the amount he gets with annual compounding is 1100*1.048^6=$1457.34

In total , for $( 5000+1100) = $6100  of investment , he gets $(6980+1457.34)= $8437.34.

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Had he invested the first sum also in monthly compounding interest, he would have got for $5000, an amount of 5000*1.0055^72=$7421.29. And his total amount of $6100 in 2  investments would have brought him an amount of $(7421.29+1466.29) = $8887.58 incuding the interest.

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Had he invested the first sum also in monthly compounding interest, he would have got for $5000, an amount of 5000*1.0055^72=$7421.29  ..........................(1)

Had he deposited a sum of $1100 every year for six 6 years  for compounding annually at the rate of 4.8% (=0.048 per dollar), then he would have got $1100*(1.048^6+1.048^5+1.048^4+1.048^3+1.048^2+1.048^1)

=$1108*x{x^5+x^4+x^3+x^2+x^1), where x=1.048

=$1108*x(x^6-1)/(x-1),

=$1100{7.092623993}

= $7801.89    ..............................................(2)

So, the 2nd invetment brings :  $7801.89-$7421.29 = $380.60 more.

Hope this helps. Any queries?