Question

Assume you purchased a house on January 1, 2020 for $200,000. You had made a down payment of 20% on the house and the balance was financed with a 30 year loan at 5% per annum stated APR with monthly payments to be made beginning January 1, 2020. What are your monthly payments?

Answer 1

$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