An auto repair shop borrowed ?$12,000 to be repaid by monthly payments over 6 years

a) Computation of Size of Periodic Payment using PMT Function in Excel:

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

Here,

PMT = Size of Periodic Payment = ?

Rate = 3%/12 = 0.25% 

Nper = 6 years * 12 months = 72 months

PV = $12,000

FV = 0

Substituting the values in formula:

=pmt(0.25%,72,-12000,0)

PMT or Size of Periodic Payment = $182.32

b) Computation of Outstanding principal after payment 22:

Total Payments = 6 * 12 months = 72 Payments

After 22 payment from 72 payments left = 72 - 22 = 50 payments

Principal after 22 payments = Find the PV for rest 50 payments using PV Function in Excel:

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

Here,

PV = PV of Rest 50 payments = ?

Rate = 3%/12 = 0.25%

Nper = 50

PMT = $182.32

FV = 0

Substituting the values in formula:

=-pv(0.25%,50,182.32,0)

PV or PV of Rest 50 Payments = $8,559.42

So, Outstanding principal after payment 22 is $8,559.42

c) Computation of Interest paid on payment 23?:

 Interest paid on payment 23 = Oustanding principal*Rate

= $8,559.42*0.25% 

= $21.40

d) Computation of Principal repaid in Payment 23:

Principal repaid in Payment 23 = Monthly payment - Interest payment on 23

= $182.32 - $21.40

Principal Paid on payment 23 = $160.93