Answer:
after the first quota carrying value: 16.360,85
after the fourht quota carrying value: 4,442.34
Explanation:
we calculate the present valeu of the payment to know the value of the car:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 4,700
time 5
rate 0.058
[tex]4700 \times \frac{1-(1+0.058)^{-5} }{0.058} = PV\\[/tex]
PV $19,906.29
Nowe to know the princpal after first payment we need to know the first quoa maortization:
19,906.29 x 0.058 = 1,154.56 interest
quota - interest
4,700 - 1,154.56 = 3,545.44
19,906.29 - 3,545.44 = 16.360,85
now the last cuota, the discounted value of the cuopa will be the amount of principal we owe as afterthis payment the loan is cancelled.
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 4,700.00
time 1.00
rate 0.058
[tex]\frac{4700}{(1 + 0.058)^{1} } = PV[/tex]
PV 4,442.34
