18 The exponentiat model below represents the balance of a loan, in dollars,
years from now. What is meaning of 1.07 in the model?

Ask by Reeves Watkins. in the United States

Jan 23,2025

Question

18 The exponentiat model below represents the balance of a loan, in dollars, $$ x $$ years from now. What is meaning of 1.07 in the model? $$ f(x)=17198(1.07)^{x} $$

UpStudy AI · Accepted Answer

In the exponential model for the loan balance:

$$ f(x) = 17,\!198 \times (1.07)^x $$

- **$$ f(x) $$** represents the balance of the loan in dollars after $$ x $$ years.
- **$$ 17,\!198 $$** is the initial loan amount.
- **$$ 1.07 $$** is the **annual growth factor**.

### Meaning of 1.07:

- **Interest Rate Interpretation**: The number **1.07** breaks down into **1** (the original principal) plus **0.07** (a 7% interest rate). This means that each year, the loan balance increases by **7%**.
  
- **Growth Factor**: Specifically, **1.07** serves as the **multiplicative factor** by which the loan balance grows each year. So, every year, the current balance is multiplied by **1.07** to account for the interest accrued.

### Example:

After 1 year ($$ x = 1 $$):
$$ f(1) = 17,\!198 \times 1.07 \approx 18,\!302.86 $$

This shows that the loan balance increases by 7% after one year.

### Summary:

**1.07** in the model represents the **7% annual interest rate**, indicating that the loan balance grows by 7% each year.
In the loan balance model $$ f(x) = 17,\!198 \times (1.07)^x $$, the **1.07** represents a **7% annual interest rate**. This means the loan balance increases by 7% each year.

18 The exponentiat model below represents the balance of a loan, in dollars,
years from now. What is meaning of 1.07 in the model?

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18 The exponentiat model below represents the balance of a loan, in dollars, years from now. What is meaning of 1.07 in the model?