Question

In: Finance

(use equations, not computer) Suppose that you are given the option to borrow a fixed rate...

(use equations, not computer)
Suppose that you are given the option to borrow a fixed rate US mortgage of $80,000 at 12% for 25 years with monthly payments. Alternatively, you may borrow another fixed rate US mortgage of $90,000 for 25 years with monthly payments at a contract interest rate to be determined. The lender would like to have an effective annual yield of 25% on the incremental cost of borrowing (i.e., on the $10,0000), reflecting the borrower’s increased default risk. Formulate how you would compute the contract interest rate on the entire $90,000 loan.

Solutions

Expert Solution

Effective monthly interest rate of the 12% p.a. mortgage=
(1+mthly rate)^12-1=12%
(1+mthly rate)=((0.12+1)^(1/12))
Mthly rate=((0.12+1)^(1/12))-1
0.009488793
0.9489%
As the lender would like to have an effective annual yield of 25% on the incremental cost of borrowing
Effective monthly interest rate of the incremental $ 10000 at 25% p.a. mortgage=
(1+mthly rate)^12-1=25%
(1+mthly rate)=((0.25+1)^(1/12))
mthly rate=((0.25+1)^(1/12))-1
0.018769
1.877%
Now, we can find the weighted average monthly interest as under:
Mortgage amt. Wt. to total Mthy.int. Wt.*mthly int.
1 2=1/$ 90000 3(as above) 4=2*3
80000 88.89% 0.009489 0.00843
10000 11.11% 0.018769 0.00209
90000 1 0.01052
Converting to annual rate
(1+0.01052)^12-1= 0.13381
ie. 13.38%
p.a.
So, the ANSWER:
The contract interest rate on the entire $90,000 loan
will be the weighted average mthly .interest ratesso as to fetch effective annual interest rates of
12% p.a.on the first $ 80000 &
25% p.a.on the incremental $ 10000
ie. 13.38%

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