To determine which investment option provides the highest future value (in 30 years), we need to calculate the future value (FV) of each investment option based on the rates and compounding periods specified. Here's the breakdown of each period and the respective interest rates.

Initial Investment: $2500

Breakdown:

1. First 10 years with George Way Services

   • Interest Rate: 5.2% compounded semi-annually (twice a year)
   • Formula: $FV = P \times \left(1 + \frac{r}{n}\right)^{nt}$
   • Where:
     • $P$ = $2500 (initial investment)
     • $r$ = 5.2% = 0.052
     • $n$ = 2 (semi-annual compounding)
     • $t$ = 10 years

2. First 10 years with Carry Heavy Towing

   • Interest Rate: 4.7% compounded monthly
   • Formula: Same formula as above
   • $P$ = $2500
   • $r$ = 4.7% = 0.047
   • $n$ = 12 (monthly compounding)
   • $t$ = 10 years

3. Next 5 years with Pontiac

   • Interest Rate: 5.7% compounded weekly
   • $P$ = Future value from either George Way or Carry Heavy Towing after 10 years (we calculate both options)
   • $r$ = 5.7% = 0.057
   • $n$ = 52 (weekly compounding)
   • $t$ = 5 years

4. Next 5 years with Applebee’s

   • Interest Rate: 6.1% compounded annually
   • $P$ = Future value after 15 years from the previous step
   • $r$ = 6.1% = 0.061
   • $n$ = 1 (annual compounding)
   • $t$ = 5 years

5. Next 15 years with Snowvalley

   • Interest Rate: 3.5% compounded quarterly
   • $P$ = Future value after 20 years
   • $r$ = 3.5% = 0.035
   • $n$ = 4 (quarterly compounding)
   • $t$ = 15 years

6. Next 15 years with Hydro One

   • Interest Rate: 2.9% compounded daily
   • $P$ = Future value after 20 years
   • $r$ = 2.9% = 0.029
   • $n$ = 365 (daily compounding)
   • $t$ = 15 years

I will calculate the future values for each investment option and compare which gives you the highest return after 30 years.Here are the future values of the initial $2500 investment after 30 years, depending on the investment strategy:

1. George Way Services (5.2% compounded semi-annually for 10 years) → Pontiac → Applebee's → Snowvalley:
   Future value after 30 years: $12,594.56

2. George Way Services (5.2% compounded semi-annually for 10 years) → Pontiac → Applebee's → Hydro One:
   Future value after 30 years: $11,536.68

3. Carry Heavy Towing (4.7% compounded monthly for 10 years) → Pontiac → Applebee's → Snowvalley:
   Future value after 30 years: $12,049.13

4. Carry Heavy Towing (4.7% compounded monthly for 10 years) → Pontiac → Applebee's → Hydro One:
   Future value after 30 years: $11,037.06

Conclusion:

The best investment over 30 years, based on these options, would be George Way Services → Pontiac → Applebee's → Snowvalley, with a final value of $12,594.56.

Would you like further details or explanations on any of these steps?

Here are 5 related questions for further learning:

1. How does compounding frequency affect the final investment outcome?
2. What is the difference between simple interest and compound interest?
3. How would different initial investments change the future value?
4. What other factors should be considered when choosing an investment strategy besides interest rates?
5. How does inflation impact long-term investments?

Tip: More frequent compounding leads to higher returns, even if the interest rate stays the same!