I could not understand the solution for the question 9.7. Can somebody help me out? A loan of £80,000 is repayable by eight annual payments, starting in one year’s time, with interest payable at 4½% pa. Payments one to three are half as much as payments four to eight. Calculate the loan outstanding one year before the loan is completely repaid. Few things I need to be clarified in particular: "Payments one to three are half as much as payments four to eight." How this is written ----> 80000 = X. a |3 + 2 X. Nu^ 3. a|5 How this is written ----> 80000 = X. a|8+X. Nu^3. a| 5 Prospectively - 2 X 7660.75Nu Retrospectively - 80000 (1+ i)^7- X. S|7 - X. S|4 Why this S|4?
So payment 1-3 is X and payment made 5-8 is 2X. So PV do all payments at start is PV of 3 yeas of X and then 5 years of 2X. Or you could think of it as X for 8 years and another X for final 5 years. At time 7, one year to go. Prospectively, PV of future payments (there's only one ) is PV of 2X. Retrospectively: we're subtracting AV of past payments (seven of them) so it's subtracting X for all 7 years and another X for 4 years, hence s4. m
what about the example in page 9?? can anyone explain how did we get 12759.16v(1+a|2) in prospective method and 50000(1.08)^2-12759.16((1.08)+1) in retrospective method
The prospective method is the PV of the future 3 repayments with the interest change after the first repayment. hence the annuity being separate from the next repayment. The retrospective method is simply the accumulated value of the loan sibtract the accumulated value of the two past repayments (they could have used s|2 but instead did it from first principles).
Hi All, Please correct me if I am wrong in the following, it is the thought process which I applied when dealing with the Example above. The prospective loan calculation determines the present value of future payments. Therefore since the payments are made in arrears at the end of each year, we can assume that after the second payment which becomes the begining of the third year. Therefore if we assume that t=2 is the point at which we want to take our PV, then the cashflow that we are seeing comes through as follows: PV= Xv1(@8%) + v^1(@8%)[ 2Xv^1(@12%) + 2Xv^2(@12%)] Solving this we get: 12759.16v(@8%)(1+a|2 (@12%)) which we can then solve. Any advice regarding the above would be wonderful. Regards N
Hi, While calculating the amount to paid for each installment, X in Q9.7, I used the following equation: 80,000= X(0.5*a3 + v^3 * a5) at 4.5% p.a. but I am getting a different answer. Why is it so? I think it should not make any difference whether we double the annuity for 5 years or half the annuity for 3 years! Kindly clarify.
Hi... When calculating the loan using retrospective method,why don't we use x and 2x..ie (1+i)^7-[xs2+2xs3]
We need the loan o/s at the end of 7th year. Using retrospective method, there are two ways: Either you can do:- 80000(1+i)^7 - X S-3(1+i)⁴ - 2X S-4 [X amt. of payments in first three years, further accumulating it to 7th year and 2X amt. of payments in next 4 years]. Or 80000(1+i)^7 - X S-7 - X S-4 [X amt. of payments in the whole 7 years plus X amt. of payments more in last 4 years i.e. from time 4 to 7 so that it makes 2X in last 4 years]. Hope this helps!
