Answer:
Ans.
A) The yield if the loan is repaid at the end of year 10 will be 6.3816%
B) The loan balance be if it is repaid after year 4 will be $66,767.48
C) The yield to the lender if the loan is repaid at the end of year 4 will be 6.6416%
Explanation:
Hi, in order to find the yield of the loan, for a 10 year period at 6% for $90,000, we would have to use MS Excel to find the cash flow and then use the "IRR" function. Please relate to the attached file to this answer for further details in the calculations.
Ans. 6.3816%
In the case of the loan balance at the end of year 4, all we need to do is to bring to year 4 all future cashflows, since there are 6 left to pay, we can use the following equation.
[tex]PresentValue(4)=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }[/tex]
Before we do that, we have to find the annual payment of the loan taking into account that the balance at the end of year 10 has to be $20,000, so we solve the following equiation for "A" before we find the present value(4). This is as follows.
[tex]90,000=\frac{A((1+0.06)^{10}-1) }{0.06(1+0.06)^{10} }+\frac{20,000}{(1+0.06)^{10} }[/tex]
[tex]90,000-\frac{20,000}{(1+0.06)^{10} }=\frac{A((1+0.06)^{10}-1) }{0.06(1+0.06)^{10}}[/tex]
[tex]78,832.10=A(7.360087051)[/tex]
[tex]A=\frac{78,832.10}{7,360087051} = 10,710.76[/tex]
Ok, now that we know this value, we use the formula to find the present value of the 6 remaining payments plus 20,000 6 periods away.
[tex]PresentValue=\frac{10,710.76((1+0.06)^{6}-1) }{0.06(1+0.06)^{6} } +\frac{20,000}{(1+0.06)^{6} }[/tex]
[tex]PresentValue=66,767.48[/tex]
As in the case of the first question, we have to use MS Excel to find out the yield to the lender if the loan is repaid at the end of year 4. So please check out the attached document.
Ans. 6.6416%
Best of luck
