When Nico was born his grandparents put $1000 in a special savings account. The amount of money in the savings account increases by 8% every year. Nico tracks how much money is in the account over time.

Question

Create a sequence that describes the amount of money in Nico’s savings each year for 8 years. (Write answers in the form or 2,000 or 1,567.87)

Use your formula to find the amount of money in Nico’s saving account after 18 years.

After 18 years Nico will have $_ in his savings account

Answer 1

To find the amount of money in Nico's savings account each year for 8 years, we can use the formula for compound interest:

$$A=P(1+r{)}^t$$

where:

• $A$ is the amount of money in the account after $t$ years,
• $P$ is the initial principal balance ($1000 in this case),
• $r$ is the annual interest rate (8%, or 0.08), and
• $t$ is the number of years the money is invested or borrowed.

Now let's calculate the amount for each year from 1 to 8:

1. Year 0 (initial deposit): $$A=1000(1+0.08{)}^0=1000$$

2. Year 1: $$A=1000(1+0.08{)}^1=1000(1.08)=1080$$

3. Year 2: $$A=1000(1+0.08{)}^2=1000({1.08}^2)=1000(1.1664)\approx 1166.40$$

4. Year 3: $$A=1000(1+0.08{)}^3=1000({1.08}^3)=1000(1.259712)\approx 1259.71$$

5. Year 4: $$A=1000(1+0.08{)}^4=1000({1.08}^4)=1000(1.36048896)\approx 1360.49$$

6. Year 5: $$A=1000(1+0.08{)}^5=1000({1.08}^5)=1000(1.469328)\approx 1469.33$$

7. Year 6: $$A=1000(1+0.08{)}^6=1000({1.08}^6)=1000(1.586874)\approx 1586.87$$

8. Year 7: $$A=1000(1+0.08{)}^7=1000({1.08}^7)=1000(1.7138)\approx 1717.99$$

9. Year 8: $$A=1000(1+0.08{)}^8=1000({1.08}^8)=1000(1.85093)\approx 1850.93$$

Now, summarizing the amounts after each year for 8 years:

• Year 0: $1,000.00
• Year 1: $1,080.00
• Year 2: $1,166.40
• Year 3: $1,259.71
• Year 4: $1,360.49
• Year 5: $1,469.33
• Year 6: $1,586.87
• Year 7: $1,717.99
• Year 8: $1,850.93

Next, let's find the amount of money in Nico's savings account after 18 years using the same formula:

$$A=1000(1+0.08{)}^{18}$$

Calculating: ${1.08}^{18}\approx 4.015$.

So: $$A=1000\times 4.015=4015.00$$

After 18 years, Nico will have $4,015.00 in his savings account.