DAY 9 – Saving Money on Your Mortgage Handout lesson Work through the handout with the students – Time will be a factor……

ASSIGN Pg. 435 #9, 10

METHODS OF SAVING INTEREST ON A MORTGAGE - Solutions 1. Making Payments more frequently. Ex. 1 You have a mortgage of $75 000 at an interest rate of 4.19%/a compounded semi-annually over an amortization period of 15 years, with a term of 5 years. a) Fill in the correct values in the following chart. b) Calculate the regular payments in the first 3 columns and the value for N in the last column. c) Calculate the total amount of interest paid in all cases. Most lending institutions allow mortgage payments to be monthly, bi-monthly (twice a month), Accelerated bi-weekly (every 2 weeks) or weekly. The difference between bi-monthly and accelerated bi-weekly is that in accelerated bi-weekly the payments are half the monthly payment. Setting

Monthly payment

Bi-monthly payment

Weekly payments

N I% PV PMT FV P/Y C/Y PMT: Total interest paid

180 4.19 75 000 -560.57 0 12 2 END

360 4.19 75 000 -280.04 0 24 2 END

780 4.19 75 000 -129.19 0 52 2 END

Accelerated bi-weekly payments (Must solve for N) 349 4.19 75 000 -280.29 0 26 2 END

25 902.13

25 814.96

25 768.06

22 896.60

In the accelerated bi-weekly case you only have to make payments for _349____ times. That is equivalent to ____13.42__ years. Conclusion: Paying more frequently __LOWER__ the amount of interest paid.

2. Shortening the Amortization Period. Ex. 2 Using the above example, find the monthly payments and the total interest paid over the following different amortization periods. Setting N I% PV PMT FV P/Y C/Y PMT: Total interest paid

25 years 300 4.19 75 000 -402.28 0 12 2 END 45 683.05

20 years 240 4.19 75 000 -460.59 0 12 2 END 35 541.48

18 years 216 4.19 75 000 -493.63 0 12 2 END 31 624.80

15 years 180 4.19 75 000 -560.57 0 12 2 END 25 902.13

Conclusion: Shortening the amortization period ___LOWERS___ the amount of interest paid.

3. Making a Lump Sum Payment. Ex. 2 A mortgage of $150 000 is amortized over 25 years with an interest rate of 8%/a compounded semi-annually. a) Calculate the monthly payment using the TVM Solver.

___-1144.82___

b) Suppose a lump sum payment of $15 000 was made at the end of the 5-year term. Determine the outstanding principal on the mortgage after the lump sum payment. Steps:

1. Determine the number of outstanding payments remaining after the 5 years 2. Calculate the present value of the remaining payments by changing the value of N to the number of outstanding payments found in step 1. Leave the other values the same as they are. Move the cursor to PV and solve for PV. PV = ___138 203.64__ Then determine the amount still owing after the lump sum payment has been made. Outstanding principal = __123 203.64__ c) Calculate, N, the number of payments remaining.

Steps:

1. Change PV to the above outstanding principal you found in part 2 above. Leave other values the same. 2. Move the cursor to N and solve. This is the number of outstanding payments remaining. Setting N I% PV PMT FV P/Y C/Y PMT:

25 years monthly payment 300 8 150 000 ? 1144.82 0 12 2 END

Finding PV

Finding N

240 8 ? 138 203.64 -1144.82 0 12 2 END

? 187 8 123 203.64 -1144.82 0 12 2 END

Notice that instead of making 240 more payments, you only have to make __187___ payments. Thus you have saved yourself __53__ monthly payments. This amounts to a savings of ____60 675.46___ over the life of the mortgage. Conclusion: Lump sum payments ___LOWERS___ the number of monthly payments remaining. 4. Paying more than the Minimum Payment. Ex. 3 You have a mortgage of $110 000 at an interest rate of 5.9%/a compounded semi-annually over an amortization period of 25 years, with a term of 5 years. a) b) c) d)

Fill in the correct values in the following chart. Calculate the regular payments in the first column. Use the value in part b) and the setting to find the value for N in the last 3 columns. Calculate the total amount of interest paid in all cases.

Setting N I% PV PMT FV P/Y C/Y PMT: Total interest paid

Monthly payment 300 5.9 110 000 -697.26 0 12 2 END

Monthly payment Plus $40 (Must solve for N) 266 5.9 110 000 -737.26 0 12 2 END

Monthly payment Plus $100 (Must solve for N) 229 5.9 110 000 -797.26 0 12 2 END

Monthly payment X 2 (Must solve for N) 100 5.9 110 000 -1394.52 0 12 2 END

99179.53

86 267.83

72 500.47

29040.25

Conclusion: Paying more than the minimum __LOWERS__ the amount of interest paid.

METHODS OF SAVING INTEREST ON A MORTGAGE 1. Making Payments more frequently. Ex. 1 You have a mortgage of $75 000 at an interest rate of 4.19%/a compounded semiannually over an amortization period of 15 years, with a term of 5 years. a) Fill in the correct values in the following chart. b) Calculate the regular payments in the first 3 columns and the value for N in the last column. c) Calculate the total amount of interest paid in all cases. Most lending institutions allow mortgage payments to be monthly, bi-monthly (twice a month), Accelerated bi-weekly (every 2 weeks) or weekly. The difference between bi-monthly and accelerated bi-weekly is that in accelerated bi-weekly the payments are half the monthly payment. Setting

Monthly payment

N I% PV PMT FV P/Y C/Y PMT: Total interest paid

180 4.19 75 000 -560.57 0 12 2 END

Bi-monthly payment

Weekly payments

Accelerated bi-weekly payments (Must solve for N)

4.19 75 000

4.19 75 000

4.19 75 000

END

END

END

25 902.13

In the accelerated bi-weekly case you only have to make payments for ___________ times. That is equivalent to ____________ years. Conclusion: Paying more frequently _________ the amount of interest paid. 2. Shortening the Amortization Period. Ex. 2 Using the above example, find the monthly payments and the total interest paid over the following different amortization periods. Setting

15 years

N I% PV PMT FV P/Y C/Y PMT: Total interest paid

180 4.19 75 000 -560.57 0 12 2 END

18 years

20 years

25 years

4.19 75 000

4.19 75 000

4.19 75 000

END

END

END

25 902.13

Conclusion: Shortening the amortization period ______________ the amount of interest paid.

3.

Making a Lump Sum Payment.

Ex. 2 A mortgage of $150 000 is amortized over 25 years with an interest rate of 8%/a compounded semi-annually. a) Calculate the monthly payment using the TVM Solver. __________________ b) Suppose a lump sum payment of $15 000 was made at the end of the 5-year term. Determine the outstanding principal on the mortgage after the lump sum payment. Steps:

1. Determine the number of outstanding payments remaining after the 5 years 2. Calculate the present value of the remaining payments by changing the value of N to the number of outstanding payments found in step 1. Leave the other values the same as they are. Move the cursor to PV and solve for PV. PV = _______________ Then determine the amount still owing after the lump sum payment has been made. Outstanding principal = _______________ c) Calculate, N, the number of payments remaining.

Steps:

1. Change PV to the above outstanding principal you found in part 2 above. Leave other values the same. 2. Move the cursor to N and solve. This is the number of outstanding payments remaining. Setting N I% PV PMT FV P/Y C/Y PMT:

25 years monthly payment 300 8 150 000 ? 1144.82 0 12 2 END

Finding PV

Finding N

8

8

? ?

12 2 END

12 2 END

Notice that instead of making 240 more payments, you only have to make _____ payments. Thus you have saved yourself ______ monthly payments. This amounts to a savings of _________ over the life of the mortgage. Conclusion: Lump sum payments ______________ the number of monthly payments remaining. 4. Paying more than the Minimum Payment. Ex. 3 You have a mortgage of $110 000 at an interest rate of 5.9%/a compounded semi-annually over an amortization period of 25 years, with a term of 5 years. a) b) c) d)

Fill in the correct values in the following chart. Calculate the regular payments in the first column. Use the value in part b) and the setting to find the value for N in the last 3 columns. Calculate the total amount of interest paid in all cases.

Setting N I% PV PMT FV P/Y C/Y PMT: Total interest paid

Monthly payment 300 5.9 110 000 -697.26 0 12 2 END

Monthly payment Plus $40 (Must solve for N)

Monthly payment Plus $100 (Must solve for N)

Monthly payment X 2 (Must solve for N)

5.9 110 000

5.9 110 000

5.9 110 000

END

END

END

99179.53

Conclusion: Paying more than the minimum ____________ __ the amount of interest paid.