Question

#1 Your local lender offers you a fixed-rate mortgage with the following terms: $250,000 at 5.25% for 30 years, monthly payments. The lender will charge you two discount points and the loan has a 4% prepayment penalty for the first 8 years of life.

C. Suppose that your effective cost over a five-year holding period is 6.50%. What amount of other fees did you pay?

Answer 1

Given that the effective cost of holding a 5 year is 6.50%.Therefore total cost=$250,000*6.5% = $16,250 p.a for a period of 5 years.=$16250*5 years=$ 81,250.

Rate of Interest given= 5.25%.

Therefore Interest payable per month=$250,000*5.25%/12=$1093.75 per month

Total Amount of interest paid in 5 years/60 months=$1093.75 * 68.74109 = $75,185.57

Note:68.74109 is the compounded interest factor for 60 months.

Therefore out of $81,250, $ 75,185.57 is the interest. Therefore Fee=$81,250 - $75,185.57= $6064.43

Detailed Calculation is as shown below

Loan Amount	Interest Rate	Interest P.a	Interest Per month	Monthly Compounding Factor	Compounded monthly interest for 5 years	Amount @6.5%
250000	0.0525	13125	1093.75	1.00	1,098.54	81250
			1093.75	1.01	1,103.34
			1093.75	1.01	1,108.17
			1093.75	1.02	1,113.02
			1093.75	1.02	1,117.89
			1093.75	1.03	1,122.78
			1093.75	1.03	1,127.69
			1093.75	1.04	1,132.62
			1093.75	1.04	1,137.58
			1093.75	1.04	1,142.55
			1093.75	1.05	1,147.55
			1093.75	1.05	1,152.57
			1093.75	1.06	1,157.62
			1093.75	1.06	1,162.68
			1093.75	1.07	1,167.77
			1093.75	1.07	1,172.88
			1093.75	1.08	1,178.01
			1093.75	1.08	1,183.16
			1093.75	1.09	1,188.34
			1093.75	1.09	1,193.54
			1093.75	1.10	1,198.76
			1093.75	1.10	1,204.00
			1093.75	1.11	1,209.27
			1093.75	1.11	1,214.56
			1093.75	1.12	1,219.88
			1093.75	1.12	1,225.21
			1093.75	1.13	1,230.57
			1093.75	1.13	1,235.96
			1093.75	1.13	1,241.36
			1093.75	1.14	1,246.79
			1093.75	1.14	1,252.25
			1093.75	1.15	1,257.73
			1093.75	1.15	1,263.23
			1093.75	1.16	1,268.76
			1093.75	1.17	1,274.31
			1093.75	1.17	1,279.88
			1093.75	1.18	1,285.48
			1093.75	1.18	1,291.11
			1093.75	1.19	1,296.76
			1093.75	1.19	1,302.43
			1093.75	1.20	1,308.13
			1093.75	1.20	1,313.85
			1093.75	1.21	1,319.60
			1093.75	1.21	1,325.37
			1093.75	1.22	1,331.17
			1093.75	1.22	1,336.99
			1093.75	1.23	1,342.84
			1093.75	1.23	1,348.72
			1093.75	1.24	1,354.62
			1093.75	1.24	1,360.54
			1093.75	1.25	1,366.50
			1093.75	1.25	1,372.48
			1093.75	1.26	1,378.48
			1093.75	1.27	1,384.51
			1093.75	1.27	1,390.57
			1093.75	1.28	1,396.65
			1093.75	1.28	1,402.76
			1093.75	1.29	1,408.90
			1093.75	1.29	1,415.06
			1093.75	1.30	1,421.25
			Total	68.74	75,185.57	6,064.43