inters rate word problem

Question

For a loan of L dollars, with an annual interest rate of r% compounded monthly, and a payment period of n months, the formula

determines the value of P, how much you would have to pay every month for the loan.

 A) A student takes a $75,000 loan at an annual rate of 6% and hopes to pay it off in 15 years. Using the formula, What would the monthly payment be? 

B) How much did they actually pay altogether? How much of that was interest?

Answer 1

Let

n = 15*12 = 180 months

r = 6% = .06

L = $75,000

Just plugin all the values and let the calculations be done in a computing machine or calculator:

(a) P = [ 75,000•.06/12 (1 + .06/12)¹⁸⁰]/[(1+.06/12)¹⁸⁰-1]

P = $632.89 is the monthly payment

(b)If a student pays $632.89 every month for 15 years (or 180 months), he will end up paying:

Total Amount = $632.89 • 180 = $113,920.67

A total interest of:

Total Interest = $113,920.67 -75,000 = $38,920.67