Actuarial Outpost Course 2 interest theory question
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#1
10-07-2002, 02:04 PM
 aas Member Join Date: May 2002 Posts: 45
Course 2 interest theory question

Hi,

Needed help with the following interest theory question:

Person takes out a loan 'L' with an interest rate of 5% and 10 repayments made at the end of each year. He uses a sinking fund to pay down the principal on this loan. THe sinking fund interest rate is 6% for repayments 1 thru 5, and 7% for the remaining payments.

What is the original amount of the loan, 'L' ?

possible solution:

[L/(s(10)@6%)]*[s(5)@6%]*(1.07)^5 + Z*(s(5)@7%) = L

where s(#) is the s angle future annuity and Z is a SF payment amount for payments 6 thru 10. If this solution is correct, I do not know what Z is. I dont know if any other info is missing-such as if the value of Z needs to be provided to solve this problem.

Thanx for any assistance
#2
10-07-2002, 03:25 PM
 retaker Member Join Date: Aug 2002 Posts: 395

From the first statement:

P = L/a_10@5%

From the second:

R=L/(s_5@6%*1.07^5 + s_5@7%) (assuming a level SF payment - R)

Unless there is some relation between P and R, I think you need more info.
#3
10-07-2002, 05:41 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,560

I agree with retaker that you need more info. You don't necessarily need any info about P (using retaker's symbols). For example, if you were told that each year the combination of the interest he pays on the loan plus the sinking fund deposit is 4000, that would be sufficient.

I suppose you are right to interpret "The sinking fund interest rate is 6% for repayments 1 thru 5, and 7% for the remaining payments" as the fund earns 6% in years 1-5 and 7% in years 6-10. It's awful wording if that is the intent, since repayment 5 never has a 6% interest rate applied to it.
#4
10-07-2002, 05:46 PM
 retaker Member Join Date: Aug 2002 Posts: 395

hey you're right, Gandolf. (as usual) I didn't notice that, but I bet that is what they meant.

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