QuestionJune 2, 2025

12. How much interest will you pay during the 14^th year of a 350,000 house price, 15 year, 6.5% monthly compounded, 80 LTV loan? None of these are valid answers 2779.11 7755.94 14,627.41 13,968.37

12. How much interest will you pay during the 14^th year of a 350,000 house price, 15 year, 6.5% monthly compounded, 80 LTV loan? None of these are valid answers 2779.11 7755.94 14,627.41 13,968.37
12. How much interest will you pay during the 14^th year of a 350,000 house price, 15 year, 6.5% monthly compounded, 80 LTV loan? None of these are valid answers 2779.11 7755.94 14,627.41 13,968.37

Solution
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Answer

None of these are valid answers Explanation 1. Calculate Loan Amount Loan-to-Value (LTV) is 80%, so loan amount = 0.8 \times 350,000 = \280,000. 2. Calculate Monthly Interest Rate Annual rate is 6.5%, so monthly rate = \frac{6.5\%}{12} = 0.5417\% = 0.005417. 3. Calculate Monthly Payment Use formula for monthly payment: **M = P \frac{r(1+r)^n}{(1+r)^n - 1}**, where P = 280,000, r = 0.005417, n = 180. M = 280,000 \times \frac{0.005417(1+0.005417)^{180}}{(1+0.005417)^{180} - 1} \approx 2434.24. 4. Calculate Total Payments by Year 13 Total payments after 13 years = 2434.24 \times 12 \times 13 = 379,366.88. 5. Calculate Remaining Balance After Year 13 Use remaining balance formula: **B = P(1+r)^n - M \frac{(1+r)^n - 1}{r}** for n = 156. B = 280,000(1+0.005417)^{156} - 2434.24 \frac{(1+0.005417)^{156} - 1}{0.005417} \approx 36,876.25. 6. Calculate Interest Paid in Year 14 Interest for year 14 = B \times r \times 12 = 36,876.25 \times 0.005417 \times 12 \approx 2,394.11.

Explanation

1. Calculate Loan Amount<br /> Loan-to-Value (LTV) is 80%, so loan amount = $0.8 \times 350,000 = \$280,000$.<br /><br />2. Calculate Monthly Interest Rate<br /> Annual rate is 6.5%, so monthly rate = $\frac{6.5\%}{12} = 0.5417\% = 0.005417$.<br /><br />3. Calculate Monthly Payment<br /> Use formula for monthly payment: **$M = P \frac{r(1+r)^n}{(1+r)^n - 1}$**, where $P = 280,000$, $r = 0.005417$, $n = 180$.<br /> $M = 280,000 \times \frac{0.005417(1+0.005417)^{180}}{(1+0.005417)^{180} - 1} \approx 2434.24$.<br /><br />4. Calculate Total Payments by Year 13<br /> Total payments after 13 years = $2434.24 \times 12 \times 13 = 379,366.88$.<br /><br />5. Calculate Remaining Balance After Year 13<br /> Use remaining balance formula: **$B = P(1+r)^n - M \frac{(1+r)^n - 1}{r}$** for $n = 156$.<br /> $B = 280,000(1+0.005417)^{156} - 2434.24 \frac{(1+0.005417)^{156} - 1}{0.005417} \approx 36,876.25$.<br /><br />6. Calculate Interest Paid in Year 14<br /> Interest for year 14 = $B \times r \times 12 = 36,876.25 \times 0.005417 \times 12 \approx 2,394.11$.
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