7.3.1 If the interest rale wos $$ 10.25 \% $$ before the repo rate was adjusted by $$ 0.5 \% $$, what new interest rale and the now loan faclor be for the 20 -yoar period?

Question

UpStudy AI · Accepted Answer

To determine the **new interest rate** and the corresponding **loan factor** for a 20-year period after the repo rate adjustment, let's follow these steps:

### 1. **Determine the New Interest Rate**

- **Original Interest Rate:** 10.25%
- **Adjustment to Repo Rate:** +0.5%

Assuming the repo rate adjustment leads to an increase in the interest rate:

$$
\text{New Interest Rate} = 10.25\% + 0.5\% = 10.75\%
$$

### 2. **Calculate the Loan Factor for a 20-Year Period**

The **loan factor** (often referred to as the Capital Recovery Factor or CRF) is used to determine the annual payment required to repay a loan over a specified period at a given interest rate. The formula for CRF is:

$$
\text{CRF} = \frac{i \times (1 + i)^n}{(1 + i)^n - 1}
$$

Where:
- $$ i $$ = annual interest rate (in decimal)
- $$ n $$ = number of periods (years)

**Given:**
- $$ i = 10.75\% = 0.1075 $$
- $$ n = 20 $$ years

**Step-by-Step Calculation:**

1. **Calculate $$ (1 + i)^n $$:**

$$
(1 + 0.1075)^{20} \approx 7.736
$$

2. **Plug the values into the CRF formula:**

$$
\text{CRF} = \frac{0.1075 \times 7.736}{7.736 - 1} = \frac{0.1075 \times 7.736}{6.736}
$$

3. **Compute the Numerator and Denominator:**

$$
\text{Numerator} = 0.1075 \times 7.736 \approx 0.8316
$$
$$
\text{Denominator} = 6.736
$$

4. **Divide to find CRF:**

$$
\text{CRF} = \frac{0.8316}{6.736} \approx 0.1234 \text{ or } 12.34\%
$$

### **Summary**

- **New Interest Rate:** **10.75%**
- **Loan Factor for 20 Years:** **12.34%**

This means that for a loan with a 10.75% interest rate over 20 years, the annual payment would be approximately **12.34%** of the initial loan amount.
The new interest rate is **10.75%**. For a 20-year loan at this rate, the loan factor is **12.34%**.

7.3.1 If the interest rale wos \( 10.25 \% \) before the repo rate was adjusted by \( 0.5 \% \), what new interest rale and the now loan faclor be for the 20 -yoar period?

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Economics Questions