Question
In: Finance
Your company has just taken out a 5-year installment loan for $600,000 at a nominal rate...
Your company has just taken out a 5-year installment loan for $600,000 at a nominal rate of 12.0% but with equal end-of-month payments.
- How much will you still owe after Year 3?
- How much total interests will you pay during the first two years?
- How much principal will you pay off during Year 4?
Solutions
Expert Solution
We are given the following information:
| r | 12.00% |
| n | 5 |
| frequency | 12 |
| PV | $ 6,00,000.00 |
Frequency is 12 because we have monthly payments
We need to solve the following equation to arrive at the monthly PMT
Next we create the following table for the 5 years:
| Year | Opening Balance | Loan | PMT | Interest | Principal repayment | Closing Balance |
| 0 | $ 6,00,000.00 | $ 6,00,000.00 | ||||
| 1 | $ 6,00,000.00 | $ 13,346.67 | $ 6,000.00 | $ 7,346.67 | $ 5,92,653.33 | |
| 2 | $ 5,92,653.33 | $ 13,346.67 | $ 5,926.53 | $ 7,420.14 | $ 5,85,233.20 | |
| 3 | $ 5,85,233.20 | $ 13,346.67 | $ 5,852.33 | $ 7,494.34 | $ 5,77,738.86 | |
| 4 | $ 5,77,738.86 | $ 13,346.67 | $ 5,777.39 | $ 7,569.28 | $ 5,70,169.58 | |
| 5 | $ 5,70,169.58 | $ 13,346.67 | $ 5,701.70 | $ 7,644.97 | $ 5,62,524.61 | |
| 6 | $ 5,62,524.61 | $ 13,346.67 | $ 5,625.25 | $ 7,721.42 | $ 5,54,803.18 | |
| 7 | $ 5,54,803.18 | $ 13,346.67 | $ 5,548.03 | $ 7,798.64 | $ 5,47,004.55 | |
| 8 | $ 5,47,004.55 | $ 13,346.67 | $ 5,470.05 | $ 7,876.62 | $ 5,39,127.92 | |
| 9 | $ 5,39,127.92 | $ 13,346.67 | $ 5,391.28 | $ 7,955.39 | $ 5,31,172.53 | |
| 10 | $ 5,31,172.53 | $ 13,346.67 | $ 5,311.73 | $ 8,034.94 | $ 5,23,137.59 | |
| 11 | $ 5,23,137.59 | $ 13,346.67 | $ 5,231.38 | $ 8,115.29 | $ 5,15,022.30 | |
| 12 | $ 5,15,022.30 | $ 13,346.67 | $ 5,150.22 | $ 8,196.45 | $ 5,06,825.85 | |
| 13 | $ 5,06,825.85 | $ 13,346.67 | $ 5,068.26 | $ 8,278.41 | $ 4,98,547.44 | |
| 14 | $ 4,98,547.44 | $ 13,346.67 | $ 4,985.47 | $ 8,361.19 | $ 4,90,186.25 | |
| 15 | $ 4,90,186.25 | $ 13,346.67 | $ 4,901.86 | $ 8,444.81 | $ 4,81,741.44 | |
| 16 | $ 4,81,741.44 | $ 13,346.67 | $ 4,817.41 | $ 8,529.25 | $ 4,73,212.19 | |
| 17 | $ 4,73,212.19 | $ 13,346.67 | $ 4,732.12 | $ 8,614.55 | $ 4,64,597.64 | |
| 18 | $ 4,64,597.64 | $ 13,346.67 | $ 4,645.98 | $ 8,700.69 | $ 4,55,896.95 | |
| 19 | $ 4,55,896.95 | $ 13,346.67 | $ 4,558.97 | $ 8,787.70 | $ 4,47,109.25 | |
| 20 | $ 4,47,109.25 | $ 13,346.67 | $ 4,471.09 | $ 8,875.58 | $ 4,38,233.67 | |
| 21 | $ 4,38,233.67 | $ 13,346.67 | $ 4,382.34 | $ 8,964.33 | $ 4,29,269.34 | |
| 22 | $ 4,29,269.34 | $ 13,346.67 | $ 4,292.69 | $ 9,053.98 | $ 4,20,215.37 | |
| 23 | $ 4,20,215.37 | $ 13,346.67 | $ 4,202.15 | $ 9,144.51 | $ 4,11,070.85 | |
| 24 | $ 4,11,070.85 | $ 13,346.67 | $ 4,110.71 | $ 9,235.96 | $ 4,01,834.89 | |
| 25 | $ 4,01,834.89 | $ 13,346.67 | $ 4,018.35 | $ 9,328.32 | $ 3,92,506.57 | |
| 26 | $ 3,92,506.57 | $ 13,346.67 | $ 3,925.07 | $ 9,421.60 | $ 3,83,084.97 | |
| 27 | $ 3,83,084.97 | $ 13,346.67 | $ 3,830.85 | $ 9,515.82 | $ 3,73,569.15 | |
| 28 | $ 3,73,569.15 | $ 13,346.67 | $ 3,735.69 | $ 9,610.98 | $ 3,63,958.17 | |
| 29 | $ 3,63,958.17 | $ 13,346.67 | $ 3,639.58 | $ 9,707.09 | $ 3,54,251.09 | |
| 30 | $ 3,54,251.09 | $ 13,346.67 | $ 3,542.51 | $ 9,804.16 | $ 3,44,446.93 | |
| 31 | $ 3,44,446.93 | $ 13,346.67 | $ 3,444.47 | $ 9,902.20 | $ 3,34,544.73 | |
| 32 | $ 3,34,544.73 | $ 13,346.67 | $ 3,345.45 | $ 10,001.22 | $ 3,24,543.51 | |
| 33 | $ 3,24,543.51 | $ 13,346.67 | $ 3,245.44 | $ 10,101.23 | $ 3,14,442.28 | |
| 34 | $ 3,14,442.28 | $ 13,346.67 | $ 3,144.42 | $ 10,202.25 | $ 3,04,240.03 | |
| 35 | $ 3,04,240.03 | $ 13,346.67 | $ 3,042.40 | $ 10,304.27 | $ 2,93,935.76 | |
| 36 | $ 2,93,935.76 | $ 13,346.67 | $ 2,939.36 | $ 10,407.31 | $ 2,83,528.45 | |
| 37 | $ 2,83,528.45 | $ 13,346.67 | $ 2,835.28 | $ 10,511.38 | $ 2,73,017.07 | |
| 38 | $ 2,73,017.07 | $ 13,346.67 | $ 2,730.17 | $ 10,616.50 | $ 2,62,400.57 | |
| 39 | $ 2,62,400.57 | $ 13,346.67 | $ 2,624.01 | $ 10,722.66 | $ 2,51,677.90 | |
| 40 | $ 2,51,677.90 | $ 13,346.67 | $ 2,516.78 | $ 10,829.89 | $ 2,40,848.02 | |
| 41 | $ 2,40,848.02 | $ 13,346.67 | $ 2,408.48 | $ 10,938.19 | $ 2,29,909.83 | |
| 42 | $ 2,29,909.83 | $ 13,346.67 | $ 2,299.10 | $ 11,047.57 | $ 2,18,862.26 | |
| 43 | $ 2,18,862.26 | $ 13,346.67 | $ 2,188.62 | $ 11,158.05 | $ 2,07,704.21 | |
| 44 | $ 2,07,704.21 | $ 13,346.67 | $ 2,077.04 | $ 11,269.63 | $ 1,96,434.58 | |
| 45 | $ 1,96,434.58 | $ 13,346.67 | $ 1,964.35 | $ 11,382.32 | $ 1,85,052.26 | |
| 46 | $ 1,85,052.26 | $ 13,346.67 | $ 1,850.52 | $ 11,496.15 | $ 1,73,556.12 | |
| 47 | $ 1,73,556.12 | $ 13,346.67 | $ 1,735.56 | $ 11,611.11 | $ 1,61,945.01 | |
| 48 | $ 1,61,945.01 | $ 13,346.67 | $ 1,619.45 | $ 11,727.22 | $ 1,50,217.79 | |
| 49 | $ 1,50,217.79 | $ 13,346.67 | $ 1,502.18 | $ 11,844.49 | $ 1,38,373.30 | |
| 50 | $ 1,38,373.30 | $ 13,346.67 | $ 1,383.73 | $ 11,962.94 | $ 1,26,410.36 | |
| 51 | $ 1,26,410.36 | $ 13,346.67 | $ 1,264.10 | $ 12,082.56 | $ 1,14,327.80 | |
| 52 | $ 1,14,327.80 | $ 13,346.67 | $ 1,143.28 | $ 12,203.39 | $ 1,02,124.41 | |
| 53 | $ 1,02,124.41 | $ 13,346.67 | $ 1,021.24 | $ 12,325.42 | $ 89,798.98 | |
| 54 | $ 89,798.98 | $ 13,346.67 | $ 897.99 | $ 12,448.68 | $ 77,350.30 | |
| 55 | $ 77,350.30 | $ 13,346.67 | $ 773.50 | $ 12,573.17 | $ 64,777.14 | |
| 56 | $ 64,777.14 | $ 13,346.67 | $ 647.77 | $ 12,698.90 | $ 52,078.24 | |
| 57 | $ 52,078.24 | $ 13,346.67 | $ 520.78 | $ 12,825.89 | $ 39,252.35 | |
| 58 | $ 39,252.35 | $ 13,346.67 | $ 392.52 | $ 12,954.15 | $ 26,298.21 | |
| 59 | $ 26,298.21 | $ 13,346.67 | $ 262.98 | $ 13,083.69 | $ 13,214.52 | |
| 60 | $ 13,214.52 | $ 13,346.67 | $ 132.15 | $ 13,214.52 | $ 0.00 | |
| $ 8,00,800.12 | $ 2,00,800.12 | $ 6,00,000.00 |
- Opening balance = previous year's closing balance
- Closing balance = Opening balance+Loan-Principal repayment
- PMT is calculated as per the above formula
- Interest = 0.12/12 x opening balance
- Principal repayment = PMT - Interest
- So in 3 years we would have made 3 x 12 = 36 monthly payment. So according to the above table, after the 36th payment, the closing balance = $2,83,528.45 ie we still owe this much at the end of 3 years
- From the above table if we sum the interest of 2 x 12 monthly
payments, we will get $1,22,154.94
so in the first two years we have paid this much of total interest. - From the above table if we sum the principal repayment for months 37 to 48 we will get $1,33,310.66 so in the 4rth year we have paid this much of principal.
Following chart shows that initially the component of interest is more while principal is less in the monthly payment which goes on reversing during the course of the loan period as we keep on repaying the principal which reduces the interest owed in each period.
jeff jeffy answered 7 months agoRelated Solutions
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