A Investment account 2 Starts with a balance of $200 and doubles everyyear. investment account 2 starts with $1,000 and increases by $100 each year.
a. How long does it take for each account to double?
b. How long does it take for each account to double again?
c. How does the growth in these two accounts compare? Explain your reasoning.
a. For investment account 1 to double, the balance needs to reach $400. Since the account doubles every year, it would take 1 year for the balance to double to $400.
For investment account 2 to double, the balance needs to reach $2,000. Since the account increases by $100 each year, it would take 10 years for the balance to reach $2,000.
b. To double again, investment account 1 would need to reach $800. Since the account doubles every year, it would take another year for the balance to reach $800.
To double again, investment account 2 would need to reach $4,000. Since the account increases by $100 each year, it would take another 10 years for the balance to reach $4,000.
c. Even though investment account 1 starts with a lower balance, it doubles every year, leading to faster growth compared to investment account 2, which increases by a fixed amount each year. This exponential growth in investment account 1 allows it to double in a much shorter time frame compared to the linear growth in investment account 2. As a result, investment account 1 experiences much faster growth compared to investment account 2.