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you plan to buy a $115,861 house. you have $23,202 to use as the down payment. the bank offers to loan you the remainder at 18% nominal interest compounded monthly. the term of the loan is 20 years. what is your equal monthly loan payment?



Answer :

ayune

The amount of loan from the bank is  $92,659. With 18% nominal interest, your equal monthly loan payment is $1,430

This is a present value of an annuity problem.

The amount of loan = house's price - down payment

                                 = $115,861  - $23,202 = $92,659

Since it is compounded monthly, hence, the number of periods (n):

n = 20 years x 12 = 240 months

i = interest rate per period = 0.18/12 = 0.015

The formula for the present value of an annuity is:

PV = C × (1 - (1+i)⁻ⁿ)/i

Where:

C = payment per period

Therefore,

92,659 = C (1 - (1 + 0.015)⁻²⁴⁰) / 0.015

C = 1430

Thus, you need to pay $1,430 per month for the loan.

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