Question

Straight bank loan.  

Right Bank offers EAR loans of 8.57% 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​) $215,000 for 6 ​years,

​(b​) $460,000 for 14 ​years,

or

​(c​) $1,100,000 for 28 ​years?

What is the APR for these monthly​ loans?

Answer 1

APR of these monthly payments =((1+EAR)^(1/n)-1)*n =((1+8.57%)^(1/12)-1)*12 =8.25079% or 8.25%

a) PV of loan =215000
Number of periods =6*12 =72
Monthly rate =8.25079%/12
Monthly Payment =PV/((1-(1+r)^-n)/r) =215000/(((1-(1+8.25079%/12)^-72)/(8.25079%/12))=3796.03

b. PV of loan =460000
Number of periods =14*12 =168
Monthly rate =8.25079%/12
Monthly Payment =PV/((1-(1+r)^-n)/r) =460000/(((1-(1+8.25079%/12)^-168)/(8.25079%/12))=4625.81

c. PV of loan =1100000
Number of periods =28*12 =336
Monthly rate =8.25079%/12
Monthly Payment =PV/((1-(1+r)^-n)/r) =1100000/(((1-(1+8.25079%/12)^-336)/(8.25079%/12))=8403.83