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# Monthly mortgage payments

John is purchasing a house for \$100,000, seeking a mortgage loan for \$80,000 or 80% loan to cost. He was offered a loan of at 6% fixed for 30 years. What will Johns monthly payment be? What is the mortgage constant?

5 years later they have a divorce. As part of the settlement they mutually agree to sell the property and pay off the mortgage. What would they have to pay the bank at the end of the 5 years? (60 months)

#### Solution Preview

Please refer attached file for better clarity of tables.

Solution:

Loan Amount=P=100000*80%=\$80000
Interest Rate=i=6%/12=0.50% per month
Number of periods=n=12*30=360
Monthly Payments=R=?

R=(P*i)/(1-1/(1+i)^n)
=80000*0.5%/(1-1/(1+0.5%)^360)
=\$479.64

Monthly Mortgage constant= R/P=479.64/80000=0.0059955=0.59955%

Let us make following amortization schedule.

Installment # Loan Amount Rate of Interest Interest Total Due Amt Paid Balance
1 80000.00 0.50% 400.00 80400.00 479.64 79920.36
2 79920.36 0.50% 399.60 80319.96 479.64 79840.32
3 79840.32 0.50% 399.20 80239.52 479.64 79759.88
4 79759.88 0.50% 398.80 80158.68 479.64 79679.04
5 79679.04 0.50% 398.40 80077.44 479.64 79597.80
6 79597.80 0.50% 397.99 79995.79 479.64 79516.15
7 79516.15 0.50% 397.58 79913.73 479.64 79434.09
8 79434.09 0.50% 397.17 79831.26 479.64 79351.62
9 79351.62 0.50% 396.76 79748.38 479.64 79268.74
10 79268.74 0.50% 396.34 79665.08 479.64 79185.44
11 79185.44 0.50% 395.93 79581.37 479.64 79101.73
12 79101.73 0.50% 395.51 79497.24 479.64 ...

#### Solution Summary

The solution describes the steps to calculate monthly payments and mortgage constant for a fixed rate montgage loan. It also calculates the principal amount left after 5 years of monthly payments.

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