Homework SourseSolve the problem Use an annual percentage rate table if nec
Solve the problem. Use an annual percentage rate table if necessary. Enrique has a 60-month fixed installment loan, with a monthly payment of $77.86. The amount he borrowed was $3,500.00. Instead of making his 12th payment, Enrique is paying the remaining balance on the loan How much interest will Engrique save. Use the actuarial method .
Solution
Solution:
Monthly EMI = $77.86
Amount borrowed = $3,500
Let monthly percentage rate = i
Now present value of monthly EMI at i rate will be equal to amount borrowed.
$77.86 * Cumulative PV factor at i rate for 60 periods = $3,500
Cumulative PV factor at i rate for 60 periods = 44.95247
the PV factor falls at discount rate of 1%
Therefore annual percentage rate = 1%
Loan amount balance after 11th payment = $3,004.25
Total amount to be paid at the time of 12th payment to setlle the loan = $3,004.25 + $30.04 = $3,034.29
Total interest saved = Total amount of 60 EMI - Total payment made
= ($77.86 * 60) - ($77.86*11 + $3,034.29) = $780.85
| Loan Amortization schedule | ||||
| Monthly period | EMI | Interest paid | Principal repayment | Loan balance |
| 0 | $3,500.00 | |||
| 1 | $77.86 | $35.00 | $42.86 | $3,457.14 |
| 2 | $77.86 | $34.57 | $43.29 | $3,413.85 |
| 3 | $77.86 | $34.14 | $43.72 | $3,370.13 |
| 4 | $77.86 | $33.70 | $44.16 | $3,325.97 |
| 5 | $77.86 | $33.26 | $44.60 | $3,281.37 |
| 6 | $77.86 | $32.81 | $45.05 | $3,236.32 |
| 7 | $77.86 | $32.36 | $45.50 | $3,190.83 |
| 8 | $77.86 | $31.91 | $45.95 | $3,144.88 |
| 9 | $77.86 | $31.45 | $46.41 | $3,098.46 |
| 10 | $77.86 | $30.98 | $46.88 | $3,051.59 |
| 11 | $77.86 | $30.52 | $47.34 | $3,004.25 |
| 12 | $77.86 | $30.04 | $47.82 | $2,956.43 |
| 13 | $77.86 | $29.56 | $48.30 | $2,908.13 |
| 14 | $77.86 | $29.08 | $48.78 | $2,859.35 |
| 15 | $77.86 | $28.59 | $49.27 | $2,810.09 |
| 16 | $77.86 | $28.10 | $49.76 | $2,760.33 |
| 17 | $77.86 | $27.60 | $50.26 | $2,710.07 |
| 18 | $77.86 | $27.10 | $50.76 | $2,659.31 |
| 19 | $77.86 | $26.59 | $51.27 | $2,608.05 |
| 20 | $77.86 | $26.08 | $51.78 | $2,556.27 |
| 21 | $77.86 | $25.56 | $52.30 | $2,503.97 |
| 22 | $77.86 | $25.04 | $52.82 | $2,451.15 |
| 23 | $77.86 | $24.51 | $53.35 | $2,397.80 |
| 24 | $77.86 | $23.98 | $53.88 | $2,343.92 |
| 25 | $77.86 | $23.44 | $54.42 | $2,289.50 |
| 26 | $77.86 | $22.89 | $54.97 | $2,234.53 |
| 27 | $77.86 | $22.35 | $55.51 | $2,179.02 |
| 28 | $77.86 | $21.79 | $56.07 | $2,122.95 |
| 29 | $77.86 | $21.23 | $56.63 | $2,066.32 |
| 30 | $77.86 | $20.66 | $57.20 | $2,009.12 |
| 31 | $77.86 | $20.09 | $57.77 | $1,951.35 |
| 32 | $77.86 | $19.51 | $58.35 | $1,893.00 |
| 33 | $77.86 | $18.93 | $58.93 | $1,834.07 |
| 34 | $77.86 | $18.34 | $59.52 | $1,774.56 |
| 35 | $77.86 | $17.75 | $60.11 | $1,714.44 |
| 36 | $77.86 | $17.14 | $60.72 | $1,653.72 |
| 37 | $77.86 | $16.54 | $61.32 | $1,592.40 |
| 38 | $77.86 | $15.92 | $61.94 | $1,530.47 |
| 39 | $77.86 | $15.30 | $62.56 | $1,467.91 |
| 40 | $77.86 | $14.68 | $63.18 | $1,404.73 |
| 41 | $77.86 | $14.05 | $63.81 | $1,340.92 |
| 42 | $77.86 | $13.41 | $64.45 | $1,276.47 |
| 43 | $77.86 | $12.76 | $65.10 | $1,211.37 |
| 44 | $77.86 | $12.11 | $65.75 | $1,145.62 |
| 45 | $77.86 | $11.46 | $66.40 | $1,079.22 |
| 46 | $77.86 | $10.79 | $67.07 | $1,012.15 |
| 47 | $77.86 | $10.12 | $67.74 | $944.41 |
| 48 | $77.86 | $9.44 | $68.42 | $876.00 |
| 49 | $77.86 | $8.76 | $69.10 | $806.90 |
| 50 | $77.86 | $8.07 | $69.79 | $737.11 |
| 51 | $77.86 | $7.37 | $70.49 | $666.62 |
| 52 | $77.86 | $6.67 | $71.19 | $595.43 |
| 53 | $77.86 | $5.95 | $71.91 | $523.52 |
| 54 | $77.86 | $5.24 | $72.62 | $450.89 |
| 55 | $77.86 | $4.51 | $73.35 | $377.54 |
| 56 | $77.86 | $3.78 | $74.08 | $303.46 |
| 57 | $77.86 | $3.03 | $74.83 | $228.63 |
| 58 | $77.86 | $2.29 | $75.57 | $153.06 |
| 59 | $77.86 | $1.53 | $76.33 | $76.73 |
| 60 | $77.86 | $1.13 | $76.73 | $0.00 |
