Answer:
$858.91
Explanation:
Since the first payment is due on the same day as purchasing the home, it is the case of an annuity due. Thus, the monthly payment can be calculated using the formula for PV of an annuity due which is as follows-
PV of an annuity due = Periodic Payment/Periodic Interest Rate x (1- 1/(1+PeriodicInterest Rate)^number of payments) x ( 1+Periodic Interest Rate)
Price of home = $200,000
Down payment = 20% of 200,000, or, .20 x 200,00, which equals $40,00.
Loan Amount = Price of home - down payment. $200,000-$160,00.
Annual percentage rate = 5%
Monthly interest rate = 5%/12, or 0.416%
Loan tenure=30 years
Number of payments = 30 x 12, or 360
After substituting, we get
$160,000 = Periodic payment/.416% x (1 - 1/(1+0.416%)^360) x (1+.416%)
Simplifying,
160,000 = Periodic payment/.416 x (1 - 1/4.67) x (1.004)
160,000 = Periodic payment/.416 x .776 x 1.004
Periodic payment = 160,00 x .416/.776x1.004
Periodic Payment = $858.91