Question

Straight bank loan.  Right Bank offers EAR loans of 8.74 % and requires a monthly payment on all loans. What is the APR for these monthly​ loans? What is the monthly payment for a loan of ​(a​) $235,000 for 6 ​years, ​(b​) $465,000 for 14 ​years, or ​(c​) $1,450,000 for 28 ​years?

Answer 1

EAR = Effective annual rate = 8.74%

EAR = ( 1 + APR)¹² - 1 = 0.0874

(1+APR/12 )¹² = 1.0874

1 + APR/12 = 12th Root of (1.0874) = 1.007

APR = 0.007 * 12 = 8.41%

What is the monthly payment for a loan of ​(a​) $235,000 for 6 ​years,

r = 0.0841 / 12 = 0.007008

n = number of years * 12 months = 6 * 12 = 72

Monthly payment = Principle Loan amount / PVIFA = 235000 / 56.389132 = 4167.47

PVIFA = [ 1 - (1.007008)^-72 ] / 0.007008 = 56.389132

​(b​) $465,000 for 14 ​years,

Monthly payment = 465000 / 98.549704 = 4718.43

PVIFA = [ 1 - (1.007008)^-168 ] / 0.007008 = 98.549704

here we apply n = 14 years * 12 = 168

or ​(c​) $1,450,000 for 28 ​years?

Monthly payment = 1,450,000 / 129.037402 = 11,237.05

PVIFA = [ 1 - (1.007008)^-336 ] / 0.007008 = 129.037402