Let's go through each part of the mortgage calculation step-by-step.

Given Data:

• Principal ($P$) = $80,000
• Annual interest rate ($r$) = 6% or 0.06
• Loan term ($n$) = 25 years = 300 months (25 × 12)

Formulas:

1. Monthly Payment Formula: $M = P \times \frac{r_{\text{monthly}} \times (1 + r_{\text{monthly}})^{n}}{(1 + r_{\text{monthly}})^{n} - 1}$ where:

   • $r_{\text{monthly}} = \frac{r}{12} = 0.06/12 = 0.005$.

2. Interest and Principal in Month $m$:

   • Interest for Month $m$: $I_m = B_{m-1} \times r_{\text{monthly}}$
   • Principal for Month $m$: $P_m = M - I_m$
   • Remaining balance after Month $m$: $B_m = B_{m-1} - P_m$

3. Outstanding Balance after 10 Years (120 months): Use the formula for the remaining balance: $B_m = P \times \frac{(1 + r_{\text{monthly}})^{n} - (1 + r_{\text{monthly}})^m}{(1 + r_{\text{monthly}})^{n} - 1}$

4. Total Principal and Interest Paid through 10 Years:

   • Total principal through 10 years = Original principal - Outstanding balance after 10 years.
   • Total interest paid through 10 years = Sum of all interest paid in 120 months.

Let's calculate each part step-by-step.Here's the detailed breakdown of the mortgage calculations:

a) Monthly Payments: $\text{Monthly Payment} = \$515.44$

b) Interest and Principal during Month 1:

• Interest (Month 1) = $400.00
• Principal (Month 1) = $115.44

c) Total Principal and Total Interest Paid Over 25 Years:

• Total Interest Paid = $74,632.34

d) Outstanding Loan Balance if Repaid at the End of Year 10:

• Outstanding Balance after 10 Years = $61,081.58

e) Total Interest and Principal Through Year 10:

• Total Principal Paid Through 10 Years = $18,918.42
• Total Interest Paid Through 10 Years = $42,934.52

f) Breakdown of Interest and Principal During Month 50:

• Interest (Month 50) = $368.04
• Principal (Month 50) = $147.40

Would you like further details or have any questions about these calculations?

Related Questions:

1. How does the interest portion change over time in a fixed-rate mortgage?
2. What is the impact of making extra payments on the principal of the loan?
3. How would the monthly payment change if the interest rate were different?
4. How does the loan term (years) affect the total interest paid?
5. What happens to the outstanding balance if the loan is refinanced after 10 years?

Tip: Making extra payments towards the principal can significantly reduce the total interest paid and shorten the loan term.