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?
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
A construction company signed a loan contract at 4.55% compounded semi-annually, with the provision to pay...
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