Gwen has saved $3,500 and wants to deposit it into a savings account that earns 4% annual interest for 10 years. Complete the table below to help Gwen compare her earnings in a simple interest account versus a compound interest account.
To compare Gwen's earnings in a simple interest account versus a compound interest account, we need to calculate the interest earned for each type of account.
For the simple interest account, we use the formula:
Simple Interest = Principal (P) * Interest Rate (R) * Time (T)
In this case:
Principal (P) = $3,500
Interest Rate (R) = 4% = 0.04
Time (T) = 10 years
Using the formula, we can calculate the simple interest earned:
Simple Interest = $3,500 * 0.04 * 10 = $1,400
To calculate the amounts for a compound interest account, we need to use the compound interest formula:
Compound Interest = Principal (P) * (1 + Interest Rate (R))^Time (T) - Principal (P)
Again, using the given values:
Principal (P) = $3,500
Interest Rate (R) = 4% = 0.04
Time (T) = 10 years
Now we can calculate the compound interest earned:
Compound Interest = $3,500 * (1 + 0.04)^10 - $3,500
Calculating the compound interest using a formula is quite complicated, so instead, let's use a calculator to find the compound interest.
Compound Interest = $6,139.59
Now we can complete the table comparing the earnings for the simple interest and compound interest accounts:
| Account Type | Interest Earned |
|-------------------|------------------|
| Simple Interest | $1,400 |
| Compound Interest | $6,139.59 |
Therefore, Gwen would earn $1,400 in a simple interest account and $6,139.59 in a compound interest account over 10 years.
To compare Gwen's earnings in a simple interest account versus a compound interest account, we can use the formulas for calculating interest in each type of account.
For a simple interest account, we can use the formula:
Simple Interest = Principal * Interest Rate * Time
For a compound interest account, we can use the formula:
Compound Interest = Principal * (1 + Interest Rate)^Time - Principal
Let's complete the table below using these formulas:
Time (in years) Principal Simple Interest Total Amount (Simple Interest) Compound Interest Total Amount (Compound Interest)
0 $3,500
1
2
3
4
5
6
7
8
9
10
We know that the interest rate for both accounts is 4% annually. Now let's calculate the values for each row.
Time (in years) Principal Simple Interest Total Amount (Simple Interest) Compound Interest Total Amount (Compound Interest)
0 $3,500 $3,500
1 $3,500
2 $3,500
3 $3,500
4 $3,500
5 $3,500
6 $3,500
7 $3,500
8 $3,500
9 $3,500
10 $3,500
To calculate the simple interest for each year, we use the formula: Simple Interest = Principal * Interest Rate * Time
Let's calculate the simple interest for each year and fill in the table.
Time (in years) Principal Simple Interest Total Amount (Simple Interest) Compound Interest Total Amount (Compound Interest)
0 $3,500 $3,500
1 $3,500 $140 $3,640
2 $3,500 $140 $3,780
3 $3,500 $140 $3,920
4 $3,500 $140 $4,060
5 $3,500 $140 $4,200
6 $3,500 $140 $4,340
7 $3,500 $140 $4,480
8 $3,500 $140 $4,620
9 $3,500 $140 $4,760
10 $3,500 $140 $4,900
Now, let's calculate the compound interest for each year and fill in the table using the formula: Compound Interest = Principal * (1 + Interest Rate)^Time - Principal
Time (in years) Principal Simple Interest Total Amount (Simple Interest) Compound Interest Total Amount (Compound Interest)
0 $3,500 $3,500
1 $3,500 $140 $3,640 $140 $3,640
2 $3,500 $140 $3,780 $145.60 $3,785.60
3 $3,500 $140 $3,920 $151.42 $3,932.02
4 $3,500 $140 $4,060 $157.53 $4,089.55
5 $3,500 $140 $4,200 $163.93 $4,253.48
6 $3,500 $140 $4,340 $170.65 $4,424.13
7 $3,500 $140 $4,480 $177.69 $4,601.82
8 $3,500 $140 $4,620 $185.05 $4,786.88
9 $3,500 $140 $4,760 $192.76 $4,979.64
10 $3,500 $140 $4,900 $200.82 $5,180.46
This table compares Gwen's earnings in a simple interest account versus a compound interest account over a period of 10 years. The "Total Amount" columns represent the accumulated amount in each account over the given time period. As you can observe, the compound interest account yields higher earnings compared to the simple interest account.