You just borrowed $700,000 using a 30 year home loan that's interest-only for the first 5 years, and principal and interest (P&I) for the remaining 25 years.The interest rate is 6.48% pa compounding monthly which is not expected to change.Which of the following statements is NOT correct?Question 5Select one:a.The effective monthly rate is 0.0054 per month, given as a decimal. If the interest rate rises, the IO and P&I monthly payments will rise.b.If the IO term was one year shorter so the P&I term was one year longer, then the monthly payments over the P&I term would be higher.c.The IO loan's perpetuity factor is 185.185185, while the P&I loan's annuity factor is 148.377206.d.The IO loan payments will be $3,780 per month, rounded to the nearest cent.e.The P&I loan payments will be $4,717.71 per month, rounded to the nearest cent.
Question
You just borrowed 700,000 using a 30 year home loan that's interest-only for the first 5 years, and principal and interest (P&I) for the remaining 25 years.The interest rate is 6.48% pa compounding monthly which is not expected to change.Which of the following statements is NOT correct?Question 5Select one:a.The effective monthly rate is 0.0054 per month, given as a decimal. If the interest rate rises, the IO and P&I monthly payments will rise.b.If the IO term was one year shorter so the P&I term was one year longer, then the monthly payments over the P&I term would be higher.c.The IO loan's perpetuity factor is 185.185185, while the P&I loan's annuity factor is 148.377206.d.The IO loan payments will be 3,780 per month, rounded to the nearest cent.e.The P&I loan payments will be $4,717.71 per month, rounded to the nearest cent.
Solution
To answer this question, we need to calculate and verify each statement one by one.
a. The effective monthly rate is calculated by dividing the annual interest rate by 12. So, 6.48% / 12 = 0.54% or 0.0054 in decimal form. This statement is correct.
b. If the interest-only term was one year shorter and the principal and interest term was one year longer, the monthly payments over the P&I term would indeed be higher because you would be spreading the repayment of the principal over a longer period. This statement is correct.
c. The perpetuity factor for an interest-only loan is calculated as 1 / monthly interest rate. So, 1 / 0.0054 = 185.185185. The annuity factor for a P&I loan is calculated using the formula [1 - (1 + r)^-n] / r, where r is the monthly interest rate and n is the number of payments. Using r = 0.0054 and n = 25*12 = 300, we get an annuity factor of 148.377206. This statement is correct.
d. The monthly payments for an interest-only loan are calculated as the loan amount multiplied by the monthly interest rate. So, 3,780. This statement is correct.
e. The monthly payments for a P&I loan are calculated as the loan amount multiplied by the monthly interest rate divided by the annuity factor. So, 25.71. This statement is incorrect.
So, the statement that is NOT correct is e. The P&I loan payments will be $4,717.71 per month, rounded to the nearest cent.
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