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Homework answers / question archive / To pay for college, you borrowed $ 1000 loan from the Government High Education Fund that makes you pay $ 126 per year for 25 years
To pay for college, you borrowed $ 1000 loan from the Government High Education Fund that makes you pay $ 126 per year for 25 years. However, you don't have to start making these payments until you graduate from the college two years from now. Calculate the yield to maturity. Why yield to maturity is important in pricing loans in financial system? Note: Your answers should be detailed with proper references. 4. Ahmad as a financial advisor has given you the following advice. "Long term bonds are the greatest investment because their interest rate is over 20%”. Is Ahmad, necessarily right? Justify your answer. Note: Your answers should be detailed with proper references.
As per the Chegg guidlines only question 3 will be answered.
Loan amount: $1000
Yearly repayment : $126 for 25 years
Yield to maturity is predominantly used in share market. When an investor is confused about which security or bond to purchase, he will use Yield to maturity. This tool is helful in understanding which choice would return with better revenue. In case of pricing loans, the yield to maturity helps to
Yield to Maturity formula: Mishkin has illustrated this yield to maturity formula for four types of debts in his book titled "The Economics of Money Banking and Financial Markets"
From this book it could be found that for a fixed rate payment loan, the Yield to maturity is solve for 'i' in the Present value formula. That interest rate which solves the present value with a given fixed loan due.
Present value = Cash flow/ (1+i)t. Here, i is the interest rate and t is the number of years.
In our case, we need to find i. Interest rate here is a fixed rate throughout the years of loan repayment.
1000 = 126/ (1+i)25
as it is difficult to solve the above equation, there are pre calculated tables available. Or else, simply we can assign arbitary values and find the right one.
| Years | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | |
| (1+i)^n | 1.118 | 1.249924 | 1.397415 | 1.56231 | 1.746663 | 1.952769 | 2.183195 | 2.440813 | 2.728828 | 3.05083 | 3.410828 | 3.813306 | 4.263276 | 4.766343 | 5.328771 | 5.957566 | 6.660559 | 7.446505 | 8.325192 | 9.307565 | 10.40586 | 11.63375 | 13.00653 | 14.5413 | 16.25718 | |
| CF/(1+i)^n | 112.7012522 | 100.8061 | 90.16648 | 80.64981 | 72.13757 | 64.52377 | 57.71357 | 51.62215 | 46.17366 | 41.30023 | 36.94118 | 33.0422 | 29.55474 | 26.43536 | 23.64523 | 21.14958 | 18.91733 | 16.92069 | 15.13479 | 13.53738 | 12.10856 | 10.83056 | 9.687441 | 8.664974 | 7.750424 | 1002.115 |
See the table above for understanding. Approximately, the 'i' value which solve for PV $1000 is 11.8%.
This yield to maturity is very important for pricing loan to determine the correct interest rate. Any value above 11.8% has resulted in different PV value than $1000. For example, when i was assumed as 12% the PV value calculated was $988.24. And when the i value was assumed as 11.5% the PV value calculated was $1023.58. Thus this tool helps the lender to know the future value and interest rate of his loan amount. He can decide either to invest in lending or other options.
