# Question on Calculus homework problem

• Nov 20th 2011, 11:14 AM
kryne
Question on Calculus homework problem
A \$300, 000 loan is to be repaid over 30 years in equal monthly installments of \$M ,
beginning at the end of the ﬁrst month. Find the monthly payment M if the loan
annual rate is 5% compounded monthly.

Hint: Find an expression for the present value of of the sum of all of the monthly
payments, set it equal to \$300,000 and solve for M .

Need to find using series I think. We haven't done anything like this in class and I looked through the book and their is nothing that will help, basically I'm 100% lost...
• Nov 20th 2011, 01:08 PM
TKHunny
Re: Question on Calculus homework problem
You MUST have SOME idea. You simply MUST. If nothing else, you could try the hint.

i = 0.05 -- This is annual interest
j = i/12 = 0.00416666... -- This is monthly interest
v = 1/(1+j) = 0.995850622406639 -- This is the monthly discount factor

That's all you need. Now build it.

300000 = M*(v + v^2 + v^3 + ... + v^360)

Can you add that up inside the parentheses?

Note: This is a geometric series.