Question

A construction company signed a loan contract at 4.55​% compounded semi-annually​, with the provision to pay ​$460 at the end of each month for four years.

​(a) What is amount of the​ loan?

​(b) How much will be owed at the end of sixteen ​months?

​(c) How much of the principal will be repaid within the first sixteen ​months?

​(d) How much interest is paid during the first sixteen ​months?

Answer 1

PMT =460
Number of months =4*12 =48
Effective monthly rate =(1+APR/2)^(1/6)-1 =(1+4.55%/2)^(1/6)-1 =0.375621660340797%

a) Amount of the loan =PMT*((1-(1+r)^-n)/r) =460*(((1-(1+0.375621660340797%)^-48)/0.375621660340797%)=
20169.3834 or 20169.38

b)Amount owed at the end of 16 months =PV*(1+r)^n-PMT*((1+r)^n-1)/r)
=20169.3834*(1+0.375621660340797%)^16-460*((1+0.375621660340797%)^16-1)/0.375621660340797%) =13845.28

c)Principal Paid in 16 months =21069.38-13845.28 =7224.10

d) Interest paid in 16 months =Number of Months *PMT -Principal Paid in 16 months =16*460-7224.10 =135.90