Question on Calculus homework problem

[kryne]

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 am totally lost...

 

[galactus]

This look like a typical interest problem. The formula can be derived through series.

\(\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}\)

Find A and divide by 360 to find the monthly payment.

 

[TchrWill]

The formula for calculating a monthly loan payment is R = Pi/[1 - 1/(1+i)^n] where R = the periodic payment, P = the principal, or debt to be paid off, n = the number of payment periods over which the payments will take place, and i = the periodic interest rate in decimal form. The interest rate for a loan is usually quoted as an annual rate such as 8%. In the formula the first thing we do is convert this to i = .08 when considering annual payments.



If payments are to be made monthly, i = .08/12 = .006666 as the monthly interest rate. An example will illustrate the use of the formula.
Lets say you want to borrow $10,000 for a home improvement, to be paid off monthly over a period of 5 years, with an annual interest rate of 8%. So P = 10,000, n = 5 x 12 = 60, i = .08/12 = .006666. Then we have R = 10000(.006666)/[1 - 1/(1+.006666)^60] = 66.66/[1 - 1/(1.489790] = 66.66/.328764 = $202.76 per month. Over the life of the loan you will pay $12,165.49 back to the bank thereby incurring the cost of $2,165.49 for the priviledge of borrowing the money.

For your given values, P = $300,000, i = .05/12 = .041666..., and n = 30(12) = 360.
What do you get?