Question

a loan, amortized over 5 years, is repaid by making payments of $1200 at the end of every month. if interest rate is 3.50% compounded semi- annually, what was the loan principal?

Answer 1

APR = 3.50%
Effective annual rate = (1+0.035/2)^2-1 = 3.53063%
APR(monthly) = 12[(1.035306)1/12 - 1] =3.474749%
Monthly rate = 3.474749/12 =0.289562%
Amount of loan
Present Value Of Annuity
c= Cash Flow	1200
i= Interest Rate	0.2896%
n= Number Of Periods	60
Present Value Of An Annuity
= C*[1-(1+i)^-n]/i]
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period
= $1200[ 1-(1+0.00289562)^-60 /0.00289562]
= $1200[ 1-(1.00289562)^-60 /0.00289562]
= $1200[ (0.1593) ] /0.00289562
= $66,005.02