Question

Lucy received a loan of $8,700 at 5.75% compounded monthly. She settled the loan by making periodic payments at the end of every three months for 4 years, with the first payment made 2 years and 3 months from now. What was the size of the periodic payments?

Answer 1

Step 1 :
loan value 2 years and 3 month from now
FV= PV*(1+r)^n
Where,
FV= Future Value
PV = Present Value
r = Interest rate =5.75%/12 =0.4191666667%
n= periods in number =2.25*12 =
= $8700*( 1+0.00479167)^27
=8700*1.13777
= $9898.56
Sep 2 :	Quarterly effective interest rate
	Monthly rate = 0.4791666667%
	Effective interest rate = (1+0.004791666667)^3 -1
	=1.4444%
Step 3 :	Calculation of periodic payment
Periodic payment = [P x R x (1+R)^N]/[(1+R)^N-1]
Where,
P= Loan Amount
R= Interest rate per period =1.4444%
N= Number of periods =4*4 =16
= [ $9898.56x0.014444 x (1+0.014444)^16]/[(1+0.014444)^16 -1]
= [ $142.97480064( 1.014444 )^16] / [(1.014444 )^16 -1
=$697.34