Answer:
Ans. A) The required annual loan payment is $4,156.43; B) Halfway through the loan's life, the loans balance is $15,557 C) Percentage of the total payments toward interest is 54.56%
Explanation:
Hi, well in order to find out the required annual loan payment, we have to use the following formula and solve for A.
[tex]PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }[/tex]
Therefore
[tex]25,000=\frac{A((1+0.105)^{10}-1) }{0.105(1+0.105)^{10} }[/tex]
[tex]25,000=\frac{1.714080847}{0.284978489} A[/tex]
[tex]25,000=A(6.01477274)[/tex]
[tex]A=\frac{25,000}{6.01477274}[/tex]
[tex]A=4,156.43[/tex]
Now, half way through the loan´s life, we still have 5 payments to make, therefore the remaining balance is found by bringing to present value those 5 yearly payments, using the same equation mentioned above, this should look like this.
[tex]PresentValue=\frac{4,156.43((1+0.105)^{5}-1) }{0.105(1+0.105)^{5} }[/tex]
[tex]PresentValue=15,556.94=15,557[/tex]
In order to find the percentage torward interest of the total payments made in the first 5 years, we had to make an amortization table (please see the attachments) so we found this
Interest (first 5 years) $11,339.10
total pmt (first 5 years) $20,782.17
% of total PMTs torward interest 54.56%
This percentage was found by: (11,339.10/20,782.17)*100=54.56%
Best of luck
The corrects statements regarding the repayment of the loan of $25,000 are as follows,
The correct options are 1-C; 2-E; 3-D. The calculation of the future value and the annual repayment of the loan can be done by using the formula for compound interest and applying the given values.
The formula for the calculation of total loan amount and applying the given values will be computed as below,
[tex]\rm Total\ Loan= Principal(1+ \dfrac {r}{n}^n)^n^t\\\\\rm Total\ Loan= 25000(1+ \dfrac{0.105}{1})^1^0\\\\\rm Total\ Loan= \$67,852[/tex]
So, the interest to be paid on the loan annually will be $4156.43.
Now, if the subtraction of the first 5 years is made, it can be ascertained that the loan's remaining balance is $15,557.
Similarly, the payments of interest in the first 5 years is calculated as below where it is given that interest rate for 5 years is $11339 and the total payment of loan is $20782.17.
[tex]\rm Percentage\ of\ Interest= \dfrac{11339}{20782.17}\ x\ 100\\\\\rm Percentage\ of\ Interest= 0.5456\ x\ 100\\\\\rm Percentage\ of\ Interest= 54.56\%[/tex]
So, 54.56% was the payment of interest in repayment of such loan.
Hence, the correct options are 1-C; 2-E; 3-D which conclude that The required annual loan payment will be $4156.43, halfway through, the remaining loan balance will be $15,557 and the total interest payments in the first 5 years will be 54.56%.
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