Question

Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 10% fixed rate for 30 years, with monthly payments to begin in one month. (Ignore taxes.)

2. Assuming they pay off the loan over the 30 year period as planned, what will the total cost (principal + interest + down payment) of the house be?

A) $187,500

B) $271,996

C) $354,234

D) $473,760

E) $511,390

3. What will the outstanding balance of the loan be after ten years assuming you make the first 120 payments right on time?

A) $  99,610

B) $135,467

C) $136,407

D) $139,144

E) $170,509

4. Suppose Rob wants to pay off the loan in 15 years. How much extra must he pay each month to do so?

A) $  11.25

B) $201.99

C) $294.95

D) $311.95

E) $314.47

Answer 1

2. Solution: $511,390
Working:
N = 30* 12 = 360; i = 10/1200 = 0.833
Down payment = 37,500
Balance payment = 187500 - 37500 = 150,000
Monthly payment = 150,000 (AP, 0.83%, 360) = 150,000 * 0.0088 = 1316.60
Total cost of building = Down payment + [Monthly instalment * 360] = 37,500 + (1316.36 * 360) = 511,390

3. Solution: $136,357.32
Working:
150,000 (F/P, 0.83%,120) + 1316.60 (F/A, 0.83%, 120)
150,000 * 2.7070 - 1316.60 * 204.845
406,056.22 - 269,698.90
136,357.32

4. Solution: $294.95
Monthly payment -30 years = 150,000 (AP, 0.83%, 360) = 150,000 * 0.0088 = 1316.60
Monthly payment -15 years = 150,000 (AP, 0.83%, 180) = 150,000 * 0.0088 = 1611.91
Difference = 1611.91 - 1316.90 = 295.55