Question

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Suppose that you have just borrowed $250,000 in the form of a 30 year mortgage. The loan has an annual interest rate of 9% with monthly payments and monthly compounding. a. What will your monthly payment be for this loan? b. What will the balance on this loan be at the end of the 12th year? How much interest will you pay in the 7th year of this loan? d. How much of the 248th payment will consist of principal? 1. С. Suppose that you have just borrowed $195,000 in the form of a 10 year mortgage. The loan has an annual interest rate of 5.375% with monthly payments and monthly compounding. a. What will your monthly payment be for this loan? b. What will the balance on this loan be at the end of the 5th year? c. How much interest will you pay in the 7th year of this loan? d. How much of the 77th payment will consist of principal? 2. Suppose that you are considering a loan in which you will borrow $245,000 using a 30-year loan. The loan has an annual interest rate of 6% with monthly payments and monthly compounding. Suppose also that the lender is charging you a 0.75% origination fee, you are paying 2.25 points in order to get the 6% interest rate, and the loan has $1,275 in third-party closing costs associated with it 3. What will the effective borrowing cost be for this loan if you make all of the scheduled а. payment? b. What will the lender's yield be for this loan if you make all of the scheduled payments? c. What will the effective borrowing cost be for this loan if you pay off the loan at the end of the 7th year? Suppose that you are considering taking out an adjustable-rate mortgage with the following terms: 4. $475,000 Prime Rate (Current value is 1.55%) 235 basis points. Amount borrowed: Index rate: Margin: Periodic cap: 1.5 percentage points 5 percentage points 25 years Lifetime cap: Amortization: What will the initial monthly payment be for this loan? f the loan's interest rate adjusts every year and the prime rate increases to 2.75% by the end of the first year, what will your payment be in the second year of the loan? What is the highest interest rate that the lender could charge over the life of the loan? a. b. c. Suppose that five years ago you borrowed $500,000 using a 30-year fixed-rate mortgage with an annual interest rate of 7.00% with monthly payments and compounding. The interest rate on 30-year fixed- rate mortgages has fallen to 6.25% and you are wondering whether you should refinance the loan Refinancing costs are expected to be 4% of the new loan amount 5. of refinancing if you make What is the net present the edu payments on the а. new loan? What is the net present value of refinancing if you pay off the new loan at the end of the 6th year? How many payments do you need to make on the new loan in order for refinancing to have a positive net present value? b. C.

Answer 1

Question1

Pv

Amount of Loan

$250,000

Rate

Monthly interest =(9/12)%

0.75%

Nper

Number of months=30*12

360

a

PMT

Monthly Payment for the loan

$2,011.56

(Using PMT function of excel with rate=0.75%, Nper=360, Pv=-250000)

b

Loan Balance at end of year 12=Present Value of monthly payments during year13-30(18*12=216 months)

Rate

Monthly interest =(9/12)%

0.75%

Nper

Number of months=18*12

216

PMT

Monthly Payment for the loan

$2,011.56

PV

Loan Balance at end of year 12

$214,807.80

(Using PV function of excel with rate=0.75%, Nper=216, Pmt=-2011.56)

c

Interest You Pay in 7th Year

Loan Balance at end of year 6

$237,026.17

(Using PV function of excel with rate=0.75%, Nper=(360-72), Pmt=-2011.56)

Loan Balance at end of year 7

$234,101.14

(Using PV function of excel with rate=0.75%, Nper=(360-84), Pmt=-2011.56)

Total Principal Payment in Year 7

$2,925.03

(237026.17-234101.14)

Total amount of payment during 7th year

$24,138.68

(2011.56*12)

Total Interest Payment during 7th year

$21,213.65

(24138.68-2925.03)

d

248th payment principal

Loan Balance at end of 247th payment

$152,920.69

(Using PV function of excel with rate=0.75%, Nper=(360-247), Pmt=-2011.56)

Interest Component of 248th payment

$1,146.91

(0.75%*152920.69)

Monthly Payment

$2,011.56

Principal Component of 248th Payment

$864.65

(2011.56-1146.91)

=PMT(F5,F6,-F4) F7 A В C D Е F G Н К L M 1 2 Question1 $250,000 Amount of Loan 4 Pv Monthly interest =(9/12)% 0.75% 5 Rate Number of months-30*12 6 Nper 360 (Using PMT function of excel with rate-0.75%, Nper- 360, Pv=-250000) $2,011.56 Monthly Payment for the loan 7 РМТ a о fox =PV(F11, F12,- F13) F14 A В D Е F G H к L м 1 2 Question1 $250,000 Amount of Loan 4 Pv Monthly interest =(9/12)% 0.75% 5 Rate Number of months 30*12 6 Nper 360 (Using PMT function of excel with rate-0.75%, Nper- 360, Pv-250000) $2,011.56 Monthly Payment for the loan 7 PMT а 8 Loan Balance at end of year 12=Present Value of monthly payments during year13-30(18 12=216 months) b 9 10 Monthly interest =(9/12)% 0.75% 11 Rate Number of months-18*12 12 Nper 216 Monthly Payment for the loan Loan Balance at end of year 12 $2,011.56 13 РMT (Using PV function of excel with rate-0.75%, Nper 216, Pmt--2011.56) $214,807.80 14 PV 15 F17 =PV(F11,288,-F13) A В C E F Н K L 1 2 3 Question1 Amount of Loan $250,000 4 Pv Monthly interest =(9/12)% 0.75% 5 Rate Number of months-30*12 6 Nper 360 $2,011.56 Monthly Payment for the loan (Using PMT function of excel with rate=0.75%, Nper 360, Pv=-250000) 7 РMT 8 Loan Balance at end of year 12=Present Value of monthly payments during year13-30(18*12=216 months) 9 10 Monthly interest =(9/12)% Rate 0.75% 11 Number of months-18*12 12 Nper 216 Monthly Payment for the loan Loan Balance at end of year 12 $2,011.56 PMT 13 14 (Using PV function of excel with rate-0.75%, Nper-216, Pmt=-2011.56) PV 15 Interest You Pay in 7th Year 16 C $237,026.17Using PV function of excel with rate-0.75%, Nper-(360-72), Pmt--2011.56 Loan Balance at end of year 6 17 fix F18 =PV(F11,276,-F7) A B C D Е F G H K L M 1 2 3 Question1 $250,000 Amount of Loan 4 Pv Monthly interest (9/12)% 0.75% 5 Rate Number of months-30*12 6 Nper 360 (Using PMT function of excel with rate-0.75%, Nper - 360, Pv=250000) $2,011.56 Monthly Payment for the loan 7 PMT a Loan Balance at end of year 12=Present Value of monthly payments during year13-30(18*12=216 months) b 10 Monthly interest =(9/12)% 0.75% 11 Rate Number of months-18*12 12 Nper 216 Monthly Payment for the loan Loan Balance at end of year 12 $2,011.56 13 РМТ $214,807.80 (Using PV function of excel with rate-0.75%, Nper-216, Pmt=-2011.56) 14 PV 15 Interest You Pay in 7th Year 16 $237,026.17 Using PV function of excel with rate 0.75%, Nper (360-72), Pmt--2011.56 Loan Balance at end of year 6 17 $234,101.14 Using PV function of excel with rate-0.75%, Nper=(360-84), Pmt--2011.56 Loan Balance at end of year 7 18 19 =PV (F11,113,-F7) X F24 А В C D Е F G Н J K м 1 2 3 Question1 $250,000 Amount of Loan 4 Pv Monthly interest =(9/12)% 0.75% 5 Rate Number of months-30*12 6 Nper 360 $2,011.56 Monthly Payment for the loan (Using PMT function of excel with rate-0.75%, Nper 360, Pv-250000) 7 PMT a Loan Balance at end of year 12 Present Value of monthly payments during year13-30(18*12=216 months) b 10 Monthly interest =(9/12)% 0.75% 11 Rate Number of months-18*12 12. Nper 216 $2,011.56 Monthly Payment for the loan 13 РМТ $214,807.80 PV Loan Balance at end of year 12 (Using PV function of excel with rate-0.75%, Nper-216, Pmt--2011.56) 14 15 Interest You Pay in 7th Year Loan Balance at end of year 6 16 C $237,026.17 (Using PV function of excel with rate=0.75%, Nper=(360-72), Pmt-2011.56) $234,101.14 (Using PV function of excel with rate=0.75%, Nper=(360-84), Pmt--2011.56) $2,925.03 $24,138.68 (2011.56*12) $21,213.65 17 Loan Balance at end of year 7 18 Total Principal Payment in Year 7 (237026.17-234101. 14) 19 Total amount of payment during 7th year Total Interest Payment during 7th year 20 (24138.68-2925.03) 21 22 248th payment principal Loan Balance at end of 247th payment d 23 $152,920.69 lUsing PV function of excel with rate-0.75%, Nper (360-247), Pmt--2011.56 24 25