Certainly! Let's break down the problem and find out the necessary values step-by-step.
### b. Calculating the Interest Rate
Your parents bought a house for R780,000, and the current bond balance is R853,592.99 after paying for 20 years. We need to find the annual interest rate.
1. Principal (P): R780,000
2. Balance after 20 years (A): R853,592.99
3. Term (n): 20 years
The annual interest rate, after calculation, is:
[tex]\[ \text{Annual Interest Rate} = 0.9120\% \][/tex]
So, the annual interest rate your parents are paying is approximately 0.9120%.
### c. Calculating Monthly Payments
Next, we need to determine the monthly payments your parents are making for the bond.
1. Term (n): 20 years, which means [tex]\( n = 20 \text{ years} \times 12 \text{ months/year} = 240 \text{ months} \)[/tex]
2. Balance after 20 years (A): R853,592.99
3. Monthly Payments: [tex]\(\text{Monthly Payments} = \frac{853,592.99}{240}\)[/tex]
So, the monthly payment is calculated as:
[tex]\[
\text{Monthly Payment} = 853,592.99 \div 240 = R3556.637458333333
\][/tex]
Thus, your parents are paying approximately R3556.64 per month for the bond.
### Summary
- Annual Interest Rate: 0.9120%
- Monthly Payment: R3556.64
These are the interest rate and monthly payment your parents are dealing with for the bond.
