Question

Discussion with lenders indicates that a loan can be obtained fro 75% of a property's market value. Loan terms will probably be 8% interest, 20-year amortization (monthly payments), with the rate renegotiable after 7 years. The property is estimated to be worth $200,000.

a) How much can be borrowed?

b) What will be the annual debt service?

c) What is the expected annual loan constant?

Show all work along with the formulas you used.

Answer 1

a)

Borrowing amount:

= $200,000*75%

= $150,000

b)

	Equal monthly payment	[P×r×(1+r)^n]÷[(1+r)^n-1]
	Here,
1	Interest rate per annum	8.00%
2	Number of years	20
3	Number of compoundings per per annum	12
4 = 1÷3	Interest rate per period ( r)	0.67%
5 = 2×3	Number of periods (n)	240
	Loan amount (P)	$                                                                                                 150,000
	Equal monthly payment	$                                                                 1,254.66
		150000*0.67%*(1+0.67%)^240)/((1+0.67%)^240-1)

Annual debt service = Equal monthly payment*12

= $1,254.66

= $15,055.92

c)

Annual loan constant:

= [Interest rate/12]/(1-(1/(1+[Interest rate/12])^n))*12

= [8%/12]/(1-(1/(1+[8%/12])^240))*12

= 10.04%