If you borrow $20,000 for 5 years at an annual rate of 8%, what would the...
If you borrow $20,000 for 5 years at an annual rate of 8%, what would the MONTHLY payment be?
I keep Getting $417.43 with a Ba II Plus Calculator.
The correct Answer is: 405.53, what am I doing wrong?
Homework Answers
Answer:
We need to use Present Value Annuity formula to find out the figure.
| A = Annuity | |
| r = Interest rate | |
| n = Number of years | |
| Loan Amount | $ 20,000.00 |
| Interest rate | 8.00% |
| Monthly rate = | 0.67% |
| No.of month | 60 |
PVA = A* (1+r)^n - 1 / r*(1+r)^n
| (1+r)^n-1 = | 0.489845708 |
| (1+r)^n = | 1.489845708 |
| r*(1+r)^n = | 0.009932305 |
| (1+r)^n - 1 / r*(1+r)^n | 49.31843334 |
| 20,000 = A * 49.3184334 | |
| A = 20,000/49.3184334 | |
| A= | $ 405.53 |
| Sr.No: | Loan Beginning | Installment | Interest | Principal | Loan Balance |
| 1 | $ 20,000.00 | $ 405.53 | $ 133.33 | $ 272.19 | $ 19,727.81 |
| 2 | $ 19,727.81 | $ 405.53 | $ 131.52 | $ 274.01 | $ 19,453.80 |
| 3 | $ 19,453.80 | $ 405.53 | $ 129.69 | $ 275.84 | $ 19,177.96 |
| 4 | $ 19,177.96 | $ 405.53 | $ 127.85 | $ 277.67 | $ 18,900.29 |
| 5 | $ 18,900.29 | $ 405.53 | $ 126.00 | $ 279.53 | $ 18,620.76 |
| 6 | $ 18,620.76 | $ 405.53 | $ 124.14 | $ 281.39 | $ 18,339.37 |
| 7 | $ 18,339.37 | $ 405.53 | $ 122.26 | $ 283.27 | $ 18,056.10 |
| 8 | $ 18,056.10 | $ 405.53 | $ 120.37 | $ 285.15 | $ 17,770.95 |
| 9 | $ 17,770.95 | $ 405.53 | $ 118.47 | $ 287.05 | $ 17,483.90 |
| 10 | $ 17,483.90 | $ 405.53 | $ 116.56 | $ 288.97 | $ 17,194.93 |
| 11 | $ 17,194.93 | $ 405.53 | $ 114.63 | $ 290.90 | $ 16,904.03 |
| 12 | $ 16,904.03 | $ 405.53 | $ 112.69 | $ 292.83 | $ 16,611.20 |
| 13 | $ 16,611.20 | $ 405.53 | $ 110.74 | $ 294.79 | $ 16,316.41 |
| 14 | $ 16,316.41 | $ 405.53 | $ 108.78 | $ 296.75 | $ 16,019.66 |
| 15 | $ 16,019.66 | $ 405.53 | $ 106.80 | $ 298.73 | $ 15,720.93 |
| 16 | $ 15,720.93 | $ 405.53 | $ 104.81 | $ 300.72 | $ 15,420.21 |
| 17 | $ 15,420.21 | $ 405.53 | $ 102.80 | $ 302.73 | $ 15,117.48 |
| 18 | $ 15,117.48 | $ 405.53 | $ 100.78 | $ 304.74 | $ 14,812.74 |
| 19 | $ 14,812.74 | $ 405.53 | $ 98.75 | $ 306.78 | $ 14,505.96 |
| 20 | $ 14,505.96 | $ 405.53 | $ 96.71 | $ 308.82 | $ 14,197.14 |
| 21 | $ 14,197.14 | $ 405.53 | $ 94.65 | $ 310.88 | $ 13,886.26 |
| 22 | $ 13,886.26 | $ 405.53 | $ 92.58 | $ 312.95 | $ 13,573.31 |
| 23 | $ 13,573.31 | $ 405.53 | $ 90.49 | $ 315.04 | $ 13,258.27 |
| 24 | $ 13,258.27 | $ 405.53 | $ 88.39 | $ 317.14 | $ 12,941.13 |
| 25 | $ 12,941.13 | $ 405.53 | $ 86.27 | $ 319.25 | $ 12,621.87 |
| 26 | $ 12,621.87 | $ 405.53 | $ 84.15 | $ 321.38 | $ 12,300.49 |
| 27 | $ 12,300.49 | $ 405.53 | $ 82.00 | $ 323.52 | $ 11,976.97 |
| 28 | $ 11,976.97 | $ 405.53 | $ 79.85 | $ 325.68 | $ 11,651.29 |
| 29 | $ 11,651.29 | $ 405.53 | $ 77.68 | $ 327.85 | $ 11,323.43 |
| 30 | $ 11,323.43 | $ 405.53 | $ 75.49 | $ 330.04 | $ 10,993.39 |
| 31 | $ 10,993.39 | $ 405.53 | $ 73.29 | $ 332.24 | $ 10,661.16 |
| 32 | $ 10,661.16 | $ 405.53 | $ 71.07 | $ 334.45 | $ 10,326.70 |
| 33 | $ 10,326.70 | $ 405.53 | $ 68.84 | $ 336.68 | $ 9,990.02 |
| 34 | $ 9,990.02 | $ 405.53 | $ 66.60 | $ 338.93 | $ 9,651.09 |
| 35 | $ 9,651.09 | $ 405.53 | $ 64.34 | $ 341.19 | $ 9,309.90 |
| 36 | $ 9,309.90 | $ 405.53 | $ 62.07 | $ 343.46 | $ 8,966.44 |
| 37 | $ 8,966.44 | $ 405.53 | $ 59.78 | $ 345.75 | $ 8,620.69 |
| 38 | $ 8,620.69 | $ 405.53 | $ 57.47 | $ 348.06 | $ 8,272.63 |
| 39 | $ 8,272.63 | $ 405.53 | $ 55.15 | $ 350.38 | $ 7,922.26 |
| 40 | $ 7,922.26 | $ 405.53 | $ 52.82 | $ 352.71 | $ 7,569.54 |
| 41 | $ 7,569.54 | $ 405.53 | $ 50.46 | $ 355.06 | $ 7,214.48 |
| 42 | $ 7,214.48 | $ 405.53 | $ 48.10 | $ 357.43 | $ 6,857.05 |
| 43 | $ 6,857.05 | $ 405.53 | $ 45.71 | $ 359.81 | $ 6,497.23 |
| 44 | $ 6,497.23 | $ 405.53 | $ 43.31 | $ 362.21 | $ 6,135.02 |
| 45 | $ 6,135.02 | $ 405.53 | $ 40.90 | $ 364.63 | $ 5,770.39 |
| 46 | $ 5,770.39 | $ 405.53 | $ 38.47 | $ 367.06 | $ 5,403.33 |
| 47 | $ 5,403.33 | $ 405.53 | $ 36.02 | $ 369.51 | $ 5,033.83 |
| 48 | $ 5,033.83 | $ 405.53 | $ 33.56 | $ 371.97 | $ 4,661.86 |
| 49 | $ 4,661.86 | $ 405.53 | $ 31.08 | $ 374.45 | $ 4,287.41 |
| 50 | $ 4,287.41 | $ 405.53 | $ 28.58 | $ 376.95 | $ 3,910.47 |
| 51 | $ 3,910.47 | $ 405.53 | $ 26.07 | $ 379.46 | $ 3,531.01 |
| 52 | $ 3,531.01 | $ 405.53 | $ 23.54 | $ 381.99 | $ 3,149.02 |
| 53 | $ 3,149.02 | $ 405.53 | $ 20.99 | $ 384.53 | $ 2,764.49 |
| 54 | $ 2,764.49 | $ 405.53 | $ 18.43 | $ 387.10 | $ 2,377.39 |
| 55 | $ 2,377.39 | $ 405.53 | $ 15.85 | $ 389.68 | $ 1,987.71 |
| 56 | $ 1,987.71 | $ 405.53 | $ 13.25 | $ 392.28 | $ 1,595.43 |
| 57 | $ 1,595.43 | $ 405.53 | $ 10.64 | $ 394.89 | $ 1,200.54 |
| 58 | $ 1,200.54 | $ 405.53 | $ 8.00 | $ 397.52 | $ 803.02 |
| 59 | $ 803.02 | $ 405.53 | $ 5.35 | $ 400.17 | $ 402.84 |
| 60 | $ 402.84 | $ 405.53 | $ 2.69 | $ 402.84 | $ (0.00) |
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