Question

2-13 interest Idle P J. R. Smith plans to borrow $200,000 through a 30-year mortgage from his bank to buy a home. If the bank charges him an interest rate of 7 percent, find the (a) Monthly mortgage payment (b) Amortization schedule for the first 3 months: balance after each payment: principal and interest portions of each payment. (c) For the first 221 payments, what is the total interest paid and the total principal. (d) How much would J. R. increase his monthly payment if he reduced the loan period to 15 years, all other things constant? How much would J. R. save in total principal and interest?

Answer 1

а В A D E F 1 borrowing amount monthly interest rate $200,000 2 a 0.583% 3 months 4 360 monthly mortgage payment $1,330.60 5 6 amortization schedule b 7 monthly carrying principal interest expense mortgage amount of month repayment loan payment $199,836.06 $1,166.67 $1,165.71 $1,330.60 $163.94 1 $1,330.60 $164.89 $199,671.17 $199,505.31 10 2 $1,164.75 $1,330.60 $165.86 11 3 12 LL .. 82 st N co o

c) B8 C D E F Н monthly interest expense mortgage carrying principal (c) amount of month repayment 8 loan рayment $1,330.60 $799.80 $530.81 $136,577.27 211 203 $796.70 $1,330.60 $533.90 $136,043.37 $135,506.35 212 204 $793.59 $1,330.60 $537.02 213 205 $790.45 $1,330.60 $540.15 $134,966.20 214 206 $787.30 $1,330.60 $1,330.60 $543.30 $134,422.89 $133,876.42 215 207 $784.13 $546.47 216 208 $ 780.95 $1,330.60 $1,330.60 $1,330.60 $1,330.60 $1,330.60 $549.66 $133,326.76 217 209 $ 777.74 $552.87 $132,773.90 $132,217.81 218 210 $774.51 $ 771.27 $556.09 219 211 $559.33 $131,658.47 220 212 $131,095.88 $130,530.00 $129,960.82 $129,388.32 $768.01 $562.60 221. 213 $ 764.73 $1,330.60 $1,330.60 $565.88 222 214 $761.42 $569.18 223 215 $758.10 $1,330.60 $1,330.60 $572.50 224 216 $754.77 $ 751.41 $575.84 $128,812.48 225 217 $1,330.60 $579.20 $582.58 $128,233.28 $127,650.70 $127,064.72 226 218 $748.03 $1,330.60 227 219 $744.63 $1,330.60 $585.98 228 220 $741.21 $1,330.60 $589.39 $126,475.33 229 221 $ 73,524.67 $220,539.03 total 230 231 total interest paid $ 220,539.03 232 $ 73,524.67 total principal paid 233 234 X

$200,000 (d) borrowing amount monthly interest rate 0.583% months 360 old monthly mortgage payment $1,330.60 new months 180 monthly interest rate new monthly mortgage payment 0.583% $ 1,797.66

total payments under old plan $1,330.60 360 total payments under new plan $1,797.66* 180 $479,017.80 $323,578.18 $155,439.62 savings in total principal and interest

double check of this savings amount can be done using both amortization schedules which is given below -

Е F G Н amortization schedule (old plan) monthly interest expense mortgage carrying principal month amount of repayment loan payment $75.19 $1,330.60 $1,330.60 $1,255.42 $1,262.74 $11,633.50 $10,370.76 351 $67.86 352 $60.50 $1,330.60 $1,330.60 $1,330.60 $1,330.60 $1,270.11 $1,277.52 $9,100.65 353 $53.09 $7,823.13 354 $45.63 $38.14 $1,284.97 $1,292.47 $1,300.01 $1,307.59 $6,538.16 $5,245.70 355 356 $30.60 $1,330.60 $3,945.69 357 $23.02 $1,330.60 $2,638.10 358 $15.39 $1,315.22 $1,322.89 $479,017.80 $200,000.00 $1,330.60 $1,322.89 359 $7.72 $1,330.60 $0.00 360 $279,017.80 total

I К L M N amortization schedule (new plan) monthly principal interest carrying amount month mortgage of loan repayment expense payment $150.19 $1,797.66 $1,797.66 $1,647.47 $24,099.55 $22,442.47 $20,775.73 $19,099.27 $17,413.02 $15,716.94 $14,010.97 $12,295.04 $10,569.11 $ 8,833.10 $7,086.97 $5,330.66 166 $140.58 $1,657.08 $1,666.74 $1,676.46 167 $130.91 $1,797.66 168 $121.19 $1,797.66 169 $111.41 $1,797.66 $1,686.24 170 $101.58 $1,797.66 $1,696.08 171 $91.68 $1,797.66 $1,797.66 $1,705.97 $1,715.93 172 $81.73 173 $71.72 $1,797.66 $1,797.66 $1,725.94 174 $61.65 $1,736.00 175 $51.53 $1,797.66 $1,797.66 $1,746.13 176 $41.34 $1,756.32 $1,766.56 177 $ 31.10 $20.79 $1,797.66 $3,564.10 $1,787.23 178 $1,797.66 $1,776.87 179 $10.43 $1,797.66 $323,578.18 $1,787.23 $0.00 180 $123,578.18 $200,000.00 total payment for interest and principal under new plan $323,578.18 total payment for interest and principal under old plan $479,017.80 $155,439.62 savings in total principal and interest

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