📚 How to calculate monthly mortgage amortization payments (Question 2)

📚 How to calculate monthly mortgage amortization payments (Question 2). 📚 How to calculate monthly mortgage amortization payments (Question 3)

📚 How to calculate monthly mortgage amortization payments (Question 2) video duration 7 Minute(s) 34 Second(s), published by Study Force on 18 10 2017 - 22:16:35.

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Q
Determine the .

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Question: Joe has a $398,000 mortgage. He locks in at 4.3% interest, compounded semi-annually, amortized for 20-years.

a) Calculate his monthly mortgage payments.

b) What percent of the total paid is interest?

What you'll need:

Present value (PV)

PV=R[〖1−(1+i)〗^(−n) ]/i → solving for R gives us → R=(PV∙i)/[〖1−(1+i)〗^(−n) ]

Where:

PV=present value amount
R=regular deposit/payment
i=interest rate per compounding period
n=total number of deposits

Since you're making monthly payments, yet the interest is being compounded semi-annually, there is a discrepancy between when payments are made and when interest is compounded. As a result, we'll need to find the effective annual rate (EAR), then use the EAR to find the effective monthly rate (EMR). This will represent the interest, i, in the PV formula.

Summary: Combining the EAR and EMR formula:

i=(1+r/m)^(m/12)−1

Where:

i=interest rate per compounding period
r=rate provided per compounding period
m=frequency of compounding

Effective annual rate (EAR)
Converts a monthly rate to an effective annual rate.

k=(1+r/m)^m−1

Where:

k=Effective annual rate
m=frequency of compounding
r=rate in decimal

Effective monthly rate (EMR)
Converts an effective annual rate to a monthly one.

i=(k+1)^(1/12)−1