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 Financial Mathematics Old FM Forum

#1
10-29-2018, 10:47 PM
 Siny SOA Join Date: Aug 2018 College: University of California, Riverside Posts: 12

Hi all! Here is the problem:

Jeff obtains a mortgage loan of 55,000 to be repaid with monthly payments at the end of each month over n years. Each monthly payment is 500.38, based on a nominal interest rate of i compounded monthly, i > 0. Jeff is unable to make the first payment but makes all the other payments on time. Still, because he skipped the first payment, he owes 3,077.94 at the end of n years. Calculate i.

Why do we need to set the present values equal when we know that the present value is 55,000? In other words, what is the difference between the set up between the 3077.94vj^12n=500.38vj and 55,000 = 500.38 a angle 12n?
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#2
10-29-2018, 10:54 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,472

You have two unknowns so you need two equations.
#3
10-29-2018, 11:02 PM
 Siny SOA Join Date: Aug 2018 College: University of California, Riverside Posts: 12

I do know that, but I am having trouble understanding the concepts of the first equation and the second equation and the difference between the two. I maybe overthinking it T_T
#4
10-29-2018, 11:10 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,472

I don't know what you mean by what is the difference. One equation relates to a single payment and the other relates to all of the payments.
#5
10-29-2018, 11:31 PM
 Siny SOA Join Date: Aug 2018 College: University of California, Riverside Posts: 12

Oh!! That makes sense, I definitely over looked that. I feel so dumb now �� thanks so so so much!