Actuarial Outpost Discounting Principle
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 Financial Mathematics Old FM Forum

#1
09-11-2019, 11:06 PM
 rebel_ao CAS SOA Join Date: Aug 2019 Posts: 22
Discounting Principle

A \$40,000 loan is to be repaid in level installments at due at the end of each year. The effective interest rate is 5%. The principal contained in the third installment is \$460. To the nearest \$10, what is the amount of each installment?

Since its a loan with level installments, can I not discount the P(3) back to t=1.

By calculating interest on the loan amount and adding the discounted principal it should give me the loan payment right?

I tried this approach and my answer was off.
#2
09-12-2019, 09:09 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,366

Quote:
 Originally Posted by rebel_ao A \$40,000 loan is to be repaid in level installments at due at the end of each year. The effective interest rate is 5%. The principal contained in the third installment is \$460. To the nearest \$10, what is the amount of each installment? Since its a loan with level installments, can I not discount the P(3) back to t=1.
Yes, you could

Quote:
 By calculating interest on the loan amount and adding the discounted principal it should give me the loan payment right?
No, because it is repaid with level installments the interest portion goes down every year. So you would need to calculate interest on the remaining balance at the start of year 3, not interest on the loan amount.
#3
09-12-2019, 11:09 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 9,148

I think he is saying P(1) = 460/(1.05)^2, I(1) = 2000 so the payment is the sum. Seems right to me. Gives a loan with 36 payments.