1. Monthly interest rate to borrower = 3.2%/12 =0.0026667
No of payments = 30*12 = 360
The monthly payment by borrower (A) is given by
A/0.0026667*(1-1/1.0026667^360) = 400000
A *231.231 = 400000
A = $1729.87
Loan Amount outstanding after 7 years (23*12 =276)
= 1729.87/0.0026667*(1-1/1.0026667^276)
=$337651.31
Let the lender Charge X discount points at the closing of loan , So on net basis the loan amount given
=$400000* (1-X/100) so that net 4% effective yield is earned i.e monthly yield 1.04^(1/12)-1 = 0.00327374 is earned
So,
-400000*(1-X/100) + 1729.87/0.00327374*(1-1/1.00327374^84)+ 337651.31/1.00327374^84 =0
=> -400000*(1-X/100) + 383448.39 =0
X = 4.1379
So, Discount points charged at the closing of loan should be 4.1379% (no other charges)
If a prepayment penalty of $X is to be charged, then
-400000 + 1729.87/0.00327374*(1-1/1.00327374^84)+ 337651.31/1.00327374^84 + X/1.00327374^84 = 0
=> X = 16551.61*1.00327374^84 = $21780.79
So, a prepayment penalty of $21780.79 has to be charged to earn effective yield of 4%
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