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# loan payments

Anthony and Cleopatra have a dilemma. It seems like a good time to buy their first home but their savings are not sufficient to get the interest rate that Tony would like to pay. If they buy today they can get a loan at 7.0% APR interest compounded monthly. If they wait three years, they will have saved enough to get a loan at 5.0% APR interest compounded monthly. But the price of housing is expected to increase at 10% per year over the next three years. They presently have savings of \$50,000 that could be used for the down payment. They are saving \$1,000 a month and earn 3% APR compounded monthly on their savings. Assuming a 30 year mortgage on a home costing \$500,000, compare the monthly payments of the two options.

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Solution:

Case 1, they buy home today

Cost of home=\$500,000
Down Payment=\$50000
Desired loan amount=PV=500000-50000=\$450000
Interest Rate per month=i=7%/12=0.0.58333%
N=number of monthly payments=30*12=360
Monthly Payments=C=?

We know that PV of an ordinary equity is given ...

#### Solution Summary

Assuming a 30 year mortgage on a home costing \$500,000, compare the monthly payments of the two options in the case.

\$2.19