Question
In: Finance
Show your work. Suppose that Jenny needs to pay her personal loan of 5000 within next...
Show your work. Suppose that Jenny needs to pay her personal loan of 5000 within next three years as monthly installments. If the bank charge 12 percent interest rate. How much she needs to pay?
Solutions
Expert Solution
First we need to find out the monthly payment
We are given the following information:
| Payment | PMT | To be calculated |
| Rate of interest | r | 12.00% |
| Number of years | n | 3.00 |
| Monthly | frequency | 12.00 |
| Loan amount | PV | 5000.00 |
We need to solve the following equation to arrive at the required PMT:
So the PMT is 166.07
So now we need to calculate the total amount Jenny needs to pay = PMT x years x months
total amount Jenny needs to pay = 166.07 x 3 x 12
total amount Jenny needs to pay = $5,978.58
Below is the amortization schedule:
| Month | Opening Balance | PMT | Interest | Principal repayment | Closing Balance |
| 1 | $ 5,000.00 | $ 166.07 | $ 50.00 | $ 116.07 | $ 4,883.93 |
| 2 | $ 4,883.93 | $ 166.07 | $ 48.84 | $ 117.23 | $ 4,766.70 |
| 3 | $ 4,766.70 | $ 166.07 | $ 47.67 | $ 118.40 | $ 4,648.29 |
| 4 | $ 4,648.29 | $ 166.07 | $ 46.48 | $ 119.59 | $ 4,528.70 |
| 5 | $ 4,528.70 | $ 166.07 | $ 45.29 | $ 120.78 | $ 4,407.92 |
| 6 | $ 4,407.92 | $ 166.07 | $ 44.08 | $ 121.99 | $ 4,285.93 |
| 7 | $ 4,285.93 | $ 166.07 | $ 42.86 | $ 123.21 | $ 4,162.71 |
| 8 | $ 4,162.71 | $ 166.07 | $ 41.63 | $ 124.44 | $ 4,038.27 |
| 9 | $ 4,038.27 | $ 166.07 | $ 40.38 | $ 125.69 | $ 3,912.58 |
| 10 | $ 3,912.58 | $ 166.07 | $ 39.13 | $ 126.95 | $ 3,785.63 |
| 11 | $ 3,785.63 | $ 166.07 | $ 37.86 | $ 128.22 | $ 3,657.42 |
| 12 | $ 3,657.42 | $ 166.07 | $ 36.57 | $ 129.50 | $ 3,527.92 |
| 13 | $ 3,527.92 | $ 166.07 | $ 35.28 | $ 130.79 | $ 3,397.13 |
| 14 | $ 3,397.13 | $ 166.07 | $ 33.97 | $ 132.10 | $ 3,265.03 |
| 15 | $ 3,265.03 | $ 166.07 | $ 32.65 | $ 133.42 | $ 3,131.61 |
| 16 | $ 3,131.61 | $ 166.07 | $ 31.32 | $ 134.76 | $ 2,996.85 |
| 17 | $ 2,996.85 | $ 166.07 | $ 29.97 | $ 136.10 | $ 2,860.75 |
| 18 | $ 2,860.75 | $ 166.07 | $ 28.61 | $ 137.46 | $ 2,723.29 |
| 19 | $ 2,723.29 | $ 166.07 | $ 27.23 | $ 138.84 | $ 2,584.45 |
| 20 | $ 2,584.45 | $ 166.07 | $ 25.84 | $ 140.23 | $ 2,444.22 |
| 21 | $ 2,444.22 | $ 166.07 | $ 24.44 | $ 141.63 | $ 2,302.59 |
| 22 | $ 2,302.59 | $ 166.07 | $ 23.03 | $ 143.05 | $ 2,159.55 |
| 23 | $ 2,159.55 | $ 166.07 | $ 21.60 | $ 144.48 | $ 2,015.07 |
| 24 | $ 2,015.07 | $ 166.07 | $ 20.15 | $ 145.92 | $ 1,869.15 |
| 25 | $ 1,869.15 | $ 166.07 | $ 18.69 | $ 147.38 | $ 1,721.77 |
| 26 | $ 1,721.77 | $ 166.07 | $ 17.22 | $ 148.85 | $ 1,572.91 |
| 27 | $ 1,572.91 | $ 166.07 | $ 15.73 | $ 150.34 | $ 1,422.57 |
| 28 | $ 1,422.57 | $ 166.07 | $ 14.23 | $ 151.85 | $ 1,270.73 |
| 29 | $ 1,270.73 | $ 166.07 | $ 12.71 | $ 153.36 | $ 1,117.36 |
| 30 | $ 1,117.36 | $ 166.07 | $ 11.17 | $ 154.90 | $ 962.46 |
| 31 | $ 962.46 | $ 166.07 | $ 9.62 | $ 156.45 | $ 806.02 |
| 32 | $ 806.02 | $ 166.07 | $ 8.06 | $ 158.01 | $ 648.01 |
| 33 | $ 648.01 | $ 166.07 | $ 6.48 | $ 159.59 | $ 488.41 |
| 34 | $ 488.41 | $ 166.07 | $ 4.88 | $ 161.19 | $ 327.23 |
| 35 | $ 327.23 | $ 166.07 | $ 3.27 | $ 162.80 | $ 164.43 |
| 36 | $ 164.43 | $ 166.07 | $ 1.64 | $ 164.43 | $ 0.00 |
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