Question

The Power of Compounding Rick and Bob are two investors that are the same age and are both planning on contributing to the same investment for the next 30 years. The investment is expected to return 8% per year over the entire savings period. Rick is planning on investing $25 at the end of each week and Bob is planning on contributing only at the end of each year. How much extra cash-flow must Bob direct towards his investment each year in order to equal the compounding effect realized by Rick's savings plan?

Answer 1

FV of investments of Rick and Bob are same.
Rate per week for Risk =8%/52
Number of Periods for Rick =30*52 =1560
PMT of Rick =25
FV of Rick =FV of Bob
25*(((1+r)^n-1)/r)=PMT*((1-(1+8%)^30-1)/8%)
25*(((1+8%/52)^1560-1)/(8%/52))=PMT*((1-(1+8%)^30-1)/8%)
PMT =1434.87

Amount of extra cash flow by Bob =1434.87-52*25 =134.87