Answer:
Monthly Payment $ 515.92
Step-by-step explanation:
First we calculate the value of the loan after the four years:
We will calcualte that using the future value of an annuity of $12,000 for 4 years at 4%
[tex]C \times \frac{(1+r)^{time} -1}{rate} = FV\\[/tex]
C 12000
time 4
rate 0.04
[tex]12000 \times \frac{(1+0.04)^{4} -1}{0.04} = FV\\[/tex]
FV $50,957.57
Now we have to calculate the cuota of a 10 years loan with this value as the principal.
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV $50,957.57
time 10 years x 12 months per year = 120
rate4% per year / 12 months = monthly rate = 0.00333
[tex]50957.57 \times \frac{1-(1+0.00333)^{-120} }{0.00333} = C\\[/tex]
C $ 515.92
