You are considering a thirty-year home loan of $320,000. A prospective lender ha

Question

You are considering a thirty-year home loan of $320,000. A prospective lender has quoted an APR of 3%
(compounded monthly) plus two points. A “point” is one percent of the loan’s amount and is deducted from
the loan proceeds. Thus, for a $100,000 loan, the lender would only give you $99,000 if the lender charged
one point. However, your monthly payment would still be based on the entire $100,000 amount.
a. What would be the amount of your monthly payment on this loan?
b. How much would the lender actually give you on this loan?
c. What is the EAR on this loan? The EAR is the annual rate the equates your monthly payments to the
actual amount that you received from the lender.

Explanation / Answer

Answer for question no.a:

Home loan amount=$320,000.

Given interest rate=3%.

Term=30 years

Monthly payment.Hence the number of months payment is to be made=30*12=360 months.

PMT function is to be used PMT(rate,nper,pv,[fv],[type])

=PMT(.03/12,360,-320000,,0)

=$1,349.13.

Answer for question no.b:

Actual loan received=320000*(100-2)%

=$313,600.

Answer for question no.c:

Rate function is to be used.

Rate(nper,pmt,pv,[fv],[type])

nper=360

pmt=1,349.13

pv=$313,600

=rate(360,-1349.13,313600,,0)

=0.26%

This is the monthly rate, interest rate per year=0.26%*12

3.16%

Effective annual rate=3.16%

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