Question

You take out an $80 000 mortgage at j2 = 9% with a 25-year amortization period.

a)	Determine the monthly payment required. (Rounded up to the next dime.)

Monthly payment

$

b)	Determine the reduced final payment. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Final payment

$

c)	Determine the total interest paid during the 4th year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Total interest paid

$

d)	At the end of 4 years, you pay down an additional $2500 (no penalty).

  

i)	How much sooner will the mortgage be paid off? (Round the final answer to the nearest whole month.)

  

Mortgage be paid off  months sooner.

  

ii)	What would be the difference in total payments over the life of the mortgage? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Difference in total payments

$

Answer 1

Interest rate of j2=9% ie., semi annual compounding is equal to annual rate of 8.835748% with monthly compounding as follows:

- C 9.00% Semi annual C9 f c =((1+C5)^(1/C8))-1 A 1 2 Yearly Nominal Rate (R) Given 3 Compounding frequency Given 4 Times compounded a year (t) 5 EAR=((1+R/t)^t)-1 ((1+C2/C4)^C4)-1 6 7 Frequency 8 Times compounded a year (t) 9 Monthly rate ((1+C5)^1/08)-1 10 Yearly rate (Monthly compounding) C9*C8 9.2025% Monthly 12 0.736312% 8.835748%

Part (a):

Monthly payment (rounded up to next dime)= $663 calculated as follows:

2 A B C D 1 Monthly payments of fixed rate loan. Payments at the end of each month 3 Monthly payments (PMT) is calculated using the formula EMI=[P*r*(1+r)^n]/[(1+r)^n)-1 4 Where P= Principal (loan amount), 5 n= Number of installments. ie if N= number of years, n=N*12 6 r=Rate of interest per month in decimals ie. If R= Yearly rate, r=R/(100*12) 7 All amounts in $ 8 Given that 9 Principal (loan amount) (P)= 80,000 No. of years (N)= 25 10 Rate of interest (% p.a)= R= 8.835748 No. of months (n)= 300 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per month in decimals (r )= R/(100*12) D10/(100*12) 0.00736312 15 No. of months (n)= N*12 G9*12 300 (1+r)= 1+G14 1.00736312 (1+r)^n= G16^G10 9.0326371 18 [(1+r)^n]-1= G17-1 8.0326371 19 P*r*(1+r)^n= D9*G14*617 5320.67368 20 Monthly payments (PMT)= [P*r*(1+r)^n]/[(1+r)^n)-1 G19/618 662.381932 21 Rounded up to next dollar $ 663 22 16 17

Part (b):

Reduced final payment= Balance outstanding after 298th payment+ Interest for the next month

=$647.05+$4.76 = $651.81

Relevant portion of amortization schedule as follows:

Part (c):

Shedule of amortization Month Beginning Monthly Monthly Interest Principal End balance interest Payments component Component balance rate =Col (2)*(3) Col (4)-(5) Col (2)-(6) (2) (3) (4) (5) (6) 80000 0.00736312 663.00 589.0498667 73.95 79926.05 79926.05 0.00736312 663.00 588.5053627 74.49 79851.56 (7) 298 299 1300.47 0.00736312 647.05 0.00736312 663.00 9.575554514 651.81 4.764309732 653.42 647.05 647.05 0.00

Total interest paid during 4th year= $6,752.40 as follows:

Shedule of amortization Month Beginning Monthly Monthly Interest Principal End balance interest Payments component Component balance rate =Col (2)*(3) = Col (4)-(5) -Col (2)-(6) (1) (2) (3) (4) (5) (6) (7) 37 76964.31 0.00736312 663.00 566.6976891 96.30 76868.01 38 76868.01 0.00736312 663.00 565.9886033 97.01 76770.99 39 76770.99 0.00736312 663.00 565.2742964 97.73 76673.27 40 76673.27 0.00736312 663.00 564.55473 98.45 76574.82 41 76574.82 0.00736312 663.00 563.8298653 99.17 76475.65 42 76475.65 0.00736312 663.00 563.0996634 99.90 76375.75 43 76375.75 0.00736312 663.00 562.3640849 100.64 76275.12 44 76275.12 0.00736312 663.00 561.6230902 101.38 76173.74 45 76173.74 0.00736312 663.00 560.8766396 102.12 76071.62 46 76071.62 0.00736312 663.00 560.1246927 102.88 75968.74 47 75968.74 0.00736312 663.00 559.3672091 103.63 75865.11 48 75865.11 0.00736312 663.00 558.6041481 104.40 75760.71 Total 6752.404712

Part (d):

(i) Total repayment period (rounded to nearest whole number)= 277 month

Repayment period as per original plan= 299 months

Therefore, mortgage will be paid off 299-277=22 months earlier.

(ii) Total payment as per original plan= $663*298 + $651.81 = $ 198,234.33

     Total payment as per revised plan= $186,148.33

     Difference in total payment= $ 198,234.33 - $186,148.33 = $12,086 (Reduction)

Relevant portion of amortization schedule as below:

Month Shedule of amortization Beginning Monthly Monthly Interest Principal End balance interest Payments component Component balance rate =Col (2)*(3) -Col (4)-(5) Col (2)-(6) (2) (3) (4) (5) (6) 80000 0.00736312 663.00 589.0498667 73.95 79926.05 79926.05 0.00736312 663.00 588.5053627 74.49 79851.56 (1) (7) 1 2 47 48 49 75968.74 0.00736312 75865.11 0.00736312 73260.71 0.00736312 663.00 559.3672091 3163.00 558.6041481 663.00 539.4276602 103.63 2604.40 123.57 75865.11 73260.71 73137.14 276 1308.87 0.00736312 277 655.51 0.00736312 Total 663.00 9.637373004 660.33 4.8265834 $ 186,148.33 653.36 655.51 655.51 0.00