Question

Straight bank loan.  Right Bank offers EAR loans of 8.99 % 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​) $ 230,000 for 7 ​years, ​(b​) $ 455,000 for 12 ​years, or ​(c​) $ 1,500,000 for 32 ​years?

Answer 1

APR = m x [(1 + EAR)^1/m - 1]

= 12 x [1.0899^1/12 - 1] = 12 x [1.0072 - 1] = 12 x 0.0072 = 0.0864, or 8.64%

Annuity = [PVA x r] / [1 - (1 + r)^-n]

a). Annuity = [$230,000 x (0.0864/12)] / [1 - {1 + (0.0864/12)}^-(7*12)]

= $1,655.91 / 0.4526 = $3,658.55

b). Annuity = [$455,000 x (0.0864/12)] / [1 - {1 + (0.0864/12)}^-(12*12)]

= $3,275.83 / 0.6441 = $5,086.11

c). Annuity = [$1,500,000 x (0.0864/12)] / [1 - {1 + (0.0864/12)}^-(32*12)]

= $10,799.43 / 0.9364 = $11,533.23