Suppose you invest $[tex]$7000[/tex] in an account that earns [tex]$7 %[/tex] simple interest annually. Use this information to complete the table below. Round to the nearest cent as needed.
| Year | Starting Balance | Interest | Ending Balance |
|---|---|---|---|
| 1 | $7000 | $490 | $7490 |
| 2 | $7490 | $ | $ |
| 3 | $ | $ | $8470 |
| 4 | $8470 | $ | $ |
| 5 | $ | $490 | $ |
Answer (2)
Calculate Year 2 interest: 7490 × 0.07 = $524.30 , ending balance: 7490 + 524.30 = $8014.30 .
Calculate Year 3 starting balance: 8470 − 490 = $7980 .
Calculate Year 4 interest: 8470 × 0.07 = $592.90 , ending balance: 8470 + 592.90 = $9062.90 .
Calculate Year 5 starting balance: 8470 − 490 = $7980 , ending balance: $8470 .
The completed values are: Year 2 Interest $524.30 , Ending Balance $8014.30 ; Year 3 Starting Balance $7980 ; Year 4 Interest $592.90 , Ending Balance $9062.90 ; Year 5 Starting Balance $7980 .
Explanation
Understanding the Problem We are given an initial investment of $7000 with a simple interest rate of 7% annually. We need to complete the table for years 2 through 5, calculating the interest earned and the ending balance for each year. Simple interest means the interest is calculated only on the principal amount, not on accumulated interest.
Calculating Year 2 For Year 2:
Starting Balance: $7490
Interest: 7490 × 0.07 = $524.30
Ending Balance: 7490 + 524.30 = $8014.30
Calculating Year 3 For Year 3:
Interest: $490 (given)
Ending Balance: $8470 (given)
Starting Balance: 8470 − 490 = $7980
Calculating Year 4 For Year 4:
Starting Balance: $8470
Interest: 8470 × 0.07 = $592.90
Ending Balance: 8470 + 592.90 = $9062.90
Calculating Year 5 For Year 5:
Interest: $490 (given)
Ending Balance: $8470 (same as year 3 since the interest is constant)
Starting Balance: 8470 − 490 = $7980
Completed Table Here's the completed table:
Year
Starting Balance
Interest
Ending Balance
1
$7000
$490
$7490
2
$7490
$524.30
$8014.30
3
$7980
$490
$8470
4
$8470
$592.90
$9062.90
5
$7980
$490
$8470
Examples
Understanding simple interest is crucial for managing personal finances. For instance, when you deposit money into a savings account, the bank pays you interest. Simple interest helps you calculate how much extra money you'll earn over time. If you deposit $1000 at a 5% simple interest rate for 3 years, you'll earn $150 in interest. This concept is also applicable when calculating interest on loans, helping you understand the total cost of borrowing money.
To complete the table, calculate the interest using the simple interest formula for each year based on the starting balance. The completed table shows the interest earned and the ending balance each year. Year 2 Interest is $524.30, Year 3 Starting Balance is $8014.30, Year 4 Interest is $595.30, and Year 5 Ending Balance is $9589.60.
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