Question

You are looking at buying a home with an asking price of $250,000. Since the market is hot, you plan to put in an offer for the full asking price. You also plan to put a $40,000 down payment and finance the remainder. Your bank is offering you a 30-year loan at 4.25% APR (compounded monthly). A) Assume your first payment is made one month from today, calculate your monthly loan payment and calculate the total amount paid to the bank over the course of 30 years B) Calculate the total interest paid to the bank over the course of 30 years. C) If you pay off $1580 monthly on the loan, how many months will it take to pay off? I had wrong answers of 1064 / 3,305,423 / 2,134,211 / 387

Answer 1

a.

loan amount (P) = asking price - down payment

=250000-40000

=210000

number of total months (n) = 30*12 = 360

interest rate per month (i) =4.25%/12 =0.003541666667

equal payment formula = P* i *((1+i)^n)/((1+i)^n-1)

=210000*0.003541666667*((1+0.003541666667)^360)/(((1+0.003541666667)^360)-1)

=1033.073771

so monthly loan payment is $1033.07

Total amount paid to bank = total months * monthly payment

=360*1033.07

=371905.2

Total amount paid to bank over 30 years is $371905.20

b.

total interest paid to bank = total amount paid - loan amount

=371905.20-210000

=161905.2

So total interest paid to bank is $161905.2

c.

monthly payment = 1580

equal payment formula = P* i *((1+i)^n)/((1+i)^n-1)

1580 =210000*0.003541666667*((1+0.003541666667)^n)/(((1+0.003541666667)^n)-1)

We will calculate n by trial and error method at which equal payment is equal to $1580

Assume n = 170 months

equal payment =210000*0.003541666667*((1+0.003541666667)^170)/(((1+0.003541666667)^170)-1)

=1646.383673

Assume n = 185 months

equal payment =210000*0.003541666667*((1+0.003541666667)^185)/(((1+0.003541666667)^185)-1)

=1549.270501

interpolation formula = lower n +((upper n - lower n)*(Upper Payment - actual payment)/(upper payment - lower payment))

170 + ((185-170)*((1646.383673-1580)/(1646.383673-1549.270501))

=180.2535534

So answer is 180 moths will be taken to pay the loan off.