Compare simple interest at 7.5% and compound interest at 7.0% when $4,300 is invested for 2 years to determine which interest earning type will result in a higher balance. Find this balance.(1 point)

Question

Responses

Simple interest at 7.5% results in a higher balance of $645 after 2 years of investment.
Simple interest at 7.5% results in a higher balance of $645 after 2 years of investment.

Simple interest at 7.5% results in a higher balance of $4,923.07 after 2 years of investment.
Simple interest at 7.5% results in a higher balance of $4,923.07 after 2 years of investment.

Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.
Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.

Compound interest at 7% results in a higher balance of $4,945 after 2 years of investment.
Compound interest at 7% results in a higher balance of $4,945 after 2 years of investment.

Answer 1

To compare simple interest and compound interest, we will use the formulas for each type of interest.

1. Calculate Simple Interest:

The formula for simple interest (SI) is: $$SI=P\times r\times t$$ where:

• $P$ is the principal amount ($4,300),
• $r$ is the rate (7.5% or 0.075),
• $t$ is the time in years (2 years).

Substituting the values: $$SI=4300\times 0.075\times 2=4300\times 0.15=645$$ The total balance after 2 years with simple interest is: $$Total,Balance=P+SI=4300+645=4945$$

2. Calculate Compound Interest:

The formula for compound interest (CI) is: $$A=P\times (1+r{)}^t$$ where:

• $P$ is the principal amount ($4,300),
• $r$ is the rate (7.0% or 0.07),
• $t$ is the time in years (2 years).

Substituting the values into the formula: $$A=4300\times (1+0.07{)}^2=4300\times (1.07{)}^2$$ Calculating $(1.07{)}^2$: $$(1.07{)}^2=1.1449(\text{approximately})$$ Now calculating the total balance: $$A=4300\times 1.1449\approx 4924.67$$

Summary:

• Simple Interest total balance after 2 years = $4,945
• Compound Interest total balance after 2 years = approximately $4,924.67

Based on this calculation, simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.