Problem 1. You have just purchased a home by borrowing $400,000 for 30-years at

Question

Problem 1. You have just purchased a home by borrowing $400,000 for 30-years at a fixed APR of 3.87%. The loan payments are monthly and interest is compounded monthly.

a. What is the periodic interest rate? (I.e., what is the monthly interest rate?)

b. What is the effective annual rate on the loan? (I.e., what is the interest rate once we take into account compounding?)

c.

What is the monthly mortgage payment?

(Hint: A mortgage is just an annuity where the borrowed amount is the present value of the annuity. So, use the annuity formula, but solved for the cash flow in terms of the present value:

CF =PV×R/k 1(1+R/k)T×k)

Explanation / Answer

a)

Periodic interest rate=3.87/12=0.3225%

b)

Effective Annual rate=(1+0.3225/100)^12-1=0.039393874=3.94%

c)

Monthly rate=R/k=3.87/12=0.3225%

No of period(N)=30*12=360 months

Let Monthly cash payment be CF

PV=CF*(1/r)(1-(1/(1+r)^N))

CF=PV/[*(1/r)(1-(1/(1+r)^N))].

CF=400000/((1/0.003225)*(1-(1/(1+0.003225)^360)))=$1879.8

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