Respuesta :
Answer:
$ 251,619.37
Step-by-step explanation:
Given that :
Loan = $ 268,000
Interest rate = 4.4 % per annum
4.4%/12 months = 0.366% per month
[tex]$3/27$[/tex] : [tex]$3$[/tex] years to pay and [tex]27[/tex] years amortization
[tex]27[/tex] years x 12 months = [tex]324[/tex] months
Calculating the amount for he monthly amortization,
[tex]$A=P \times \frac{r(1+r)^n}{(1+r)^n-1}$[/tex]
[tex]$A=268,000 \times \frac{0.00366(1+0.0366)^{324}}{(1+0.00366)^{324}-1}$[/tex]
[tex]$A=268,000 \times \frac{0.0119}{2.266}$[/tex]
A = 1407.41
Therefore, the future value is given by :
[tex]$FV=PV(1+r)^n-P\left[\frac{(1+r)^n-1}{r}\right]$[/tex]
where, FV = future value ( balloon balance)
PV = present value (original balance)
P = payment
r = rate per payment
n = number of payments
[tex]$FV=268,000(1+0.00366)^{36}-1407.41\left[\frac{(1+0.00366)^{36}-1}{0.00366}\right]$[/tex]
[tex]$FV = 305670.10- 54050.73 $[/tex]
FV = 251619.37
Therefore, Stuart's balloon payment will be $ 251,619.37
