Question: We were calculating the monthly payment pay a mortgage: Annual mortgag

Question

Question: We were calculating the monthly payment pay a mortgage: Annual mortgage interest rate is 3% and after the down payment we left with $800,000.00 and we will pay back in 30 years. We calculated the monthly payment in two ways. 1st way: calculate the annual payment with annual interest rate 3%, then divided to 12. Annual Payment= PVxannual interst rate =800,000×0.03-40,815 (a+annual interest rate)i 1-10230 Monthly Amount = 401215-$3,401 which is incorrect 2nd Way: calculate the monthly interest rate first annual interest rate 12 3% 12 -0.25% a PVxmonthly interst rate to calculate the monthly payment Then use the formul (1 1) (1+monthly interest rate)" 00 00 0025$3,373 which is the correct way 800,000×0.0025 = $3,373 which is the correct way 1.0028360 We noticed that the final answers are different if we calculate it in different way, but why those two numbers are different? Explain it.

Explanation / Answer

When monthly payments are made then in that case interest has to be compounded monthly.

This means that if annual interest is given then it has to be divided by 12 to ascertain monthly interest.

This monthly interest has to be utilized to determine the annual payment. Also, time period (repayment period) has to be multiplied by 12 to ascertain repayment period in terms of months.

These two steps takes into account monthly compounding principle and thus provides the correct amount of monthly payment.

In first way, procedure of monthly compounding has not been applied. Due to this non-application, monthly amount calculated is incorrect.

On the other hand, in second way, procedure of monthly compounding has been applied. Due to this application, monthly amount calculated is correct.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.