N
Noely
Member
Hi All,
I'm having an issue with the final part of the below question.
Question: A loan of 50,000 is being repaid over a period of 10 years by a series of level monthly instalments. Interest charges on the loan are at a rate of 8%p.a. effective.
i) Calculate the monthly repayments
ii) Calculate the amount of interest paid in the first year
iii) After the payment at the end of 7 years, the borrower takes a 2-month payment break and doesn't make any payments. Calculate the extra amount he has to pay each month in order to clear his debt by the end of the 10th year.
Parts i & ii of the question are striaghtforward.
Part (iii) Solution:
Thought process:
1. Calculate the outstanding loan at time 7 (t=7)
2. Determine the interest applied over 2 months that the repayments were not made.
3. Calculate the repayment using simple equation of value.
Applying the above thought process to this problem we get the following:
Calculate the PV at t=7, we get the outstanding amount of 19203.57
Apply interest for 2 months gives us:
\(19203.57*(1.08)^(2/12) = 19451.48\)
Using the above value we can determine the equation of value as:
\[PV=I*\require{enclose}a_{\enclose{actuarial}{n}} \]
\[I* \require{enclose}a_{\enclose{actuarial}{34}} = 19451.48 \]
Therefore the new repayment:
\[I = 19451.48/\require{enclose}a_{\enclose{actuarial}{34}} = 1681.49\]
What I can't get is that in the Solution the value for \[\require{enclose}a_{\enclose{actuarial}{34}} \] becomes 30.45056, where I am getting 11.586.
Can someone please help me figure out where I mght have gone wrong?
I'm having an issue with the final part of the below question.
Question: A loan of 50,000 is being repaid over a period of 10 years by a series of level monthly instalments. Interest charges on the loan are at a rate of 8%p.a. effective.
i) Calculate the monthly repayments
ii) Calculate the amount of interest paid in the first year
iii) After the payment at the end of 7 years, the borrower takes a 2-month payment break and doesn't make any payments. Calculate the extra amount he has to pay each month in order to clear his debt by the end of the 10th year.
Parts i & ii of the question are striaghtforward.
Part (iii) Solution:
Thought process:
1. Calculate the outstanding loan at time 7 (t=7)
2. Determine the interest applied over 2 months that the repayments were not made.
3. Calculate the repayment using simple equation of value.
Applying the above thought process to this problem we get the following:
Calculate the PV at t=7, we get the outstanding amount of 19203.57
Apply interest for 2 months gives us:
\(19203.57*(1.08)^(2/12) = 19451.48\)
Using the above value we can determine the equation of value as:
\[PV=I*\require{enclose}a_{\enclose{actuarial}{n}} \]
\[I* \require{enclose}a_{\enclose{actuarial}{34}} = 19451.48 \]
Therefore the new repayment:
\[I = 19451.48/\require{enclose}a_{\enclose{actuarial}{34}} = 1681.49\]
What I can't get is that in the Solution the value for \[\require{enclose}a_{\enclose{actuarial}{34}} \] becomes 30.45056, where I am getting 11.586.
Can someone please help me figure out where I mght have gone wrong?