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 6 months agoRelated Solutions
Your company has just taken out a 1-year installment loan for $82,500 at a nominal rate...
Your company has just taken out a 1-year installment loan for
$82,500 at a nominal rate of 12.0% but with equal end-of-month
payments. What percentage of the 2nd monthly payment will go toward
the repayment of principal? 89.2% 90.5% 88.9% 88.5% 89.6%
Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate...
Your business has just taken out a 1-year installment loan for
$72,500 at a nominal rate of 6.5% but with equal end-of-month
payments. What percentage of the 2nd monthly payment will go toward
the repayment of principal?
Select the correct answer.
a. 94.23%
b. 96.23%
c. 98.23%
d. 95.23%
e. 97.23%
1. Your company has just taken out a 3-years installment loan for $1,000 at a nominal...
1. Your company has just taken out a 3-years installment loan
for $1,000 at a nominal rate of 10.0% with equal end-of-month
payments $402.11. What is the beginning balance, Interest,
Principal, and Ending balance for the year two and three?
You have just bought a house and have taken out a mortgage (an installment) loan for...
You have just bought a house and have taken out a mortgage (an
installment) loan for $500,000. This is a 30-year loan that
requires monthly payments and the first payment is due one month
from today. The APR for the loan is 24%. You are interested to know
how much of your 210th monthly payment will go toward
the repayment of principal? That amount is _______________
Question 10 options:
$762.65
$9,586.98
$625.64
$9,494.78
$513.24
$9,382.38
$421.04
$9,245.37
Ms. Jordan has just taken out a $150,000 mortgage loan at an interest rate of 6...
Ms. Jordan has just taken out a $150,000 mortgage loan
at an interest rate of 6 percent. If the
mortgage calls for equal monthly payments for 20 years,
what is the amount of each payment?
Also, work out an amortization table
You have just purchased a car and taken out a $46000 loan. The loan has a...
You have just purchased a car and taken out a $46000 loan. The
loan has a five-year term with monthly payments and an APR of 6.5
%
a. How much will you pay in interest, and how much will you pay
in principal, during the first month, second month, and first
year? (Hint: Compute the loan balance after one month, two
months, and one year.)
b. How much will you pay in interest, and how much will you pay
in...
You have just purchased a car and taken out a $50,000 loan. The loan has a...
You have just purchased a car and taken out a $50,000 loan. The
loan has a 5-year term with monthly payments and an APR of 6%. How
much will you pay in interest, and how much will you pay in
principle, during the first month and second month? (Hint:
construct an amortization table to show the breakdown of interest
and principal paid in the first two months).
You have just purchased a car and taken out a $40,000 loan. The loan has a?...
You have just purchased a car and taken out a $40,000 loan. The
loan has a? five-year term with monthly payments and an APR of 6.3
%
a. How much will you pay in? interest, and how
much will you pay in? principal, during the first? month, second?
month, and first? year? (Hint: Compute the loan balance after one?
month, two? months, and one? year.)
b. How much will you pay in? interest, and how
much will you pay in?...
You have just purchased a car and taken out a $41,000 loan. The loan has a...
You have just purchased a car and taken out a
$41,000 loan. The loan has a five-year term with monthly
payments and an APR of 6.1%.
a. How much will you pay in interest, and how much will you pay
in principal, during the first month, second month, and first
year? (Hint: Compute the loan balance after one month, two
months, and one year.)
b. How much will you pay in interest, and how much will you pay
in principal,...
You have just purchased a car and taken out a $39,000 loan. The loan has a...
You have just purchased a car and taken out a $39,000 loan. The
loan has a five-year term with monthly payments and an APR of 5.5%
. a. How much will you pay in interest, and how much will you pay
in principal, during the first month, second month, and first
year? (Hint: Compute the loan balance after one month, two
months, and one year.) b. How much will you pay in interest, and
how much will you pay in...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Iron-Bit is a manufacturer of industrial drill bits. The management is concerned about the adequacy of...
- You have 625 mL of an 0.23 M acetic acid solution. What volume (V) of 2.10...
- A change in behavior or belief to accord with others is called obedience conformity acceptance complianc
- Search for information about the Rana Plaza collapse in Bangladesh (2013)!•What happened and who is responsible...
- 1. Suppose the data for a hypothetical economy is given above. This economy produces only 3...
- The following items were in transit to or from Power Corp. on December 31, 2009 Goods...
- Suppose that you are asked to equip a desktop with a wireless NIC. Which type of...
ADVERTISEMENT