Question

You want to buy a $198,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan for the rest.

a) How much is the loan amount going to be?

$

b) What will your monthly payments be if the interest rate is 6%?

$

c) What will your monthly payments be if the interest rate is 7%?

$

Answer 1

a) How much is the loan amount going to be?

Cost of the house = $198,000

Down payment = 20% of cost of house or 20% of $198,000 = $39,600

Therefore, loan amount = Cost of the house - Down payment

= $198,000 - $39,600 = $158,400

b) What will your monthly payments be if the interest rate is 6%?

We can use present value (PV) of an Annuity formula to calculate the equal monthly payment of mortgage loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV of mortgage loan = $158,400

PMT = Monthly payment =?

n = N = number of payments = 30 years *12 months =360 month

i = I/Y = 6% per year, therefore monthly interest rate = 6%/12 = 0.5% per month

Therefore,

$158,400 = PMT* [1- (1+0.5%)^-360]/0.5%

= $949.69

Monthly payment is $949.69 for this mortgage loan    

c) What will your monthly payments be if the interest rate is 7%?

We can use present value (PV) of an Annuity formula to calculate the equal monthly payment of mortgage loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV of mortgage loan = $158,400

PMT = Monthly payment =?

n = N = number of payments = 30 years *12 months =360 month

i = I/Y = 7% per year, therefore monthly interest rate = 7%/12 = 0.5833% per month

Therefore,

$158,400 = PMT* [1- (1+0.5833%)^-360]/0.5833%

= $1,053.84

Monthly payment is $1,053.84 for this mortgage loan