Oleg has a loan for $4500 for 3 years at 3

a) Computation of Effective Monthly Interest Rate:

Effective Monthly Interest Rate = (1+r/m)^(m/n) - 1

= (1+3.75%/2)^(2/12) - 1

= (1+1.875%)^(0.1667) -1

= 1.0031 - 1

Effective Monthly Interest Rate = 0.0031 or 0.31%

b) Computation of Monthly Payments using PMT Function in Excel:

=pmt(rate,nper,-pv,fv)

Here,

PMT = Monthly Payment = ?

Rate = 0.31%

NPER = 12 months * 3 Years = 36 months

PV = $4,500

FV = 0

Substituting the values in formula:

=pmt(0.31%,36,-4500,0)

PMT or Monthly Payment = $132.30

c) Computation of Outstanding Balance on his loan after 1 year:

Outstanding Balance on his loan after 1 year = ($4,500*(1+0.31%)^12) - ($132.30*(1+0.31%)^12)

= $4,670.33 - $137.31

Outstanding Balance on his loan after 1 year = $4,533.03

d) If, at the end of 1 year, the interest rate changes to 3.25% (compounded 2 times per year), Present Value of his remaining monthly payments (at the new interest rate):

Computation of Effective Monthly Interest Rate:

Effective Monthly Interest Rate = (1+r/m)^(m/n) - 1

= (1+3.25%/2)^(2/12) - 1

= (1+1.175%)^(0.1667) -1

= 1.0029 - 1

Effective Monthly Interest Rate = 0.0029 or 0.29%

Computation of Present Value of Remaining Monthly Payments using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Present Value of Remaining Monthly Payments = ?

Rate = 0.29%

Nper = 12 Months*2 Years = 24 Months

PMT = $132.30

FV = 0

Substituting the values in formula:

=-pv(0.29%,24,132.30,0)

PV or Present Value of Remaining Monthly Payments = $3,062.94

e) Computation of New Monthly Payment at the revised interest rate using PMT Function in Excel:

=pmt(rate,nper,-pv,fv)

Here,

PMT = Monthly Payment = ?

Rate = 0.29%

NPER = 12 months * 2 Years = 24 months

PV = $4,533.03

FV = 0

Substituting the values in formula:

=pmt(0.29%,24,-4533.03,0)

PMT or Monthly Payment = $195.79