Annuity and Loan question - Please help

[navya]

ASM Practice exam 1: Q1)

A 35-yr annuity - immediate pays 1.05^35 in the first year, 1.05^34 in the second year, etc., until 1.05 is paid in the 35th year. The present value of this annuity at 5% effective is X. Determine X.

Could someone explain how this problem could be solved?

I was trying to use basic principles to do it a long way but want to find out if there is a shorter way?



Q)46 - Sample Questions

Seth borrows X for four years at an annual effective interest rate of 8%, to be repaid with equal payments at the end of each year. The outstanding loan balance at the end of the third year is 559.12.

Calculate the principal repaid in the first payment.

Answer: I understand the answer that is given but when I attempted the question I tried to do it another way which is not giving me the correct answer, could someone please tell me what is wrong with my approach. Thanks a lot.

So we are told that the outstanding balance at the end of year 3 is 559.12, the loan has to be paid off by year 4 so I interpreted that to be that the payment is equal to 559.12.

Using that I tried to use the calculator to enter the loan information and then use the Amort function to get the PR in the first payment but that did not give me the correct answer. Then secondly I tried to use the formula: PR(v^(n-k+1)) and wasn't working too.

Can either of these approaches used?

[Hexfire]

Q1 from the ASM Practice Exam seems to be a question that is aimed to see if students understand the basic concepts of obtaining a present value and summing them up in a combination of geometric progression. My edition of ASM shows the solution and does just that.

Q46

My understanding of amortization is the same as yours, that is, since B_3 = 559.12, Principal repaid in the last year of the loan is also 559.12. However, your post suggests you entered 559.12 as your Annual payment / [PMT]. My understanding is that it's Principal Repaid @ t=4. So that


(Principal Repaid @ t=4) = Pv^(4-4+1) = Pv = P(1.08^(-1)) = 559.12.

You can then solve for P and then solve for Principal Repaid @ t=1 using the same formula.

Hex~

[kahosit]

would the answer to the second one be 443.85?
if not then i don't know how to do it...sorry

[Hexfire]

It looks that way (the answer is 443.85). The loan is for 2000. Using the Amort keys 443.85 is the answer.

Hex~

[kahosit]

if that is the correct answer then here is what i did...

the outstanding balance after the 3rd payment is what was mentioned

since there is only one payment left after that then that means it is the annual payment amount

but each annual payment is at the end of the year

so then it would be that amount x the interest for a year

using that value for payment you can find the first principal repaid with the pv^(n+1-k)

[navya]

Thanks for the responses. That makes a lot more sense now.

I understood the way they explained it in the answer but wanted to figure out why could I not use the pmt (v^n-k+1) to do it. I didnt think of giving the outstanding balance interest to get payment amount.

Thanks to both of you for your help.

[zmkramer]

ASM Practice exam 1: Q1)

A 35-yr annuity - immediate pays 1.05^35 in the first year, 1.05^34 in the second year, etc., until 1.05 is paid in the 35th year. The present value of this annuity at 5% effective is X. Determine X.

Could someone explain how this problem could be solved?

I was trying to use basic principles to do it a long way but want to find out if there is a shorter way?



Q)46 - Sample Questions

Seth borrows X for four years at an annual effective interest rate of 8%, to be repaid with equal payments at the end of each year. The outstanding loan balance at the end of the third year is 559.12.

Calculate the principal repaid in the first payment.

Answer: I understand the answer that is given but when I attempted the question I tried to do it another way which is not giving me the correct answer, could someone please tell me what is wrong with my approach. Thanks a lot.

So we are told that the outstanding balance at the end of year 3 is 559.12, the loan has to be paid off by year 4 so I interpreted that to be that the payment is equal to 559.12.

Using that I tried to use the calculator to enter the loan information and then use the Amort function to get the PR in the first payment but that did not give me the correct answer. Then secondly I tried to use the formula: PR(v^(n-k+1)) and wasn't working too.

Can either of these approaches used?


for the first one using first principals you should see that the present value is equal to s[18/10.25%] + a[17/10.25%] that is the quickest way to do the problem.

the second problem:

your outstanding balance for the loan (amortization method) is the present value of your remaining payments at that point in time.

so if they give you the OB at 3 years on a 4 year loan that means that the OB is the value of the last payment discounted 1 year at the loan interest rate. 559.12*1.08 = the payment

so you take the payment and multiply by v^5-t for the principal repaid for time t. and that should give you the answer