Question

You want to buy a $249,000 home. You plan to pay 15% 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 5%? $

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

Answer 1

a)

Calculation of loan amount;

 

Formula;

Loan amount = Home value * (1 - Down payment)

Loan amount = $249,000 * (1 - 0.15)

Loan amount = $249,000 * 0.85

Loan amount = $211,650

 

Loan amount = $211,650.

 

b)

Calculation of monthly payments be if the interest rate is 5%:

 

Formula;

Monthly payment = P * r * (1 + r)^n / [(1 + r)^n - 1]

Where;

P = Principal loan amount i.e. $211,650

r = Monthly interest rate i.e. 0.00416666666666667 (0.05 / 12)

n = Monthly period of loan i.e. 360 (30 Years * 12)

 

Now put values in the formula;

Monthly payment = $211650 * 0.00416666666666667 * (1 + 0.00416666666666667)^360 / [(1 + 0.00416666666666667)^360 - 1]

Monthly payment = $881.875 * 1.00416666666666667^360 / (1.00416666666666667^360 - 1)

Monthly payment = $881.875 * 4.46774431400616 / (4.46774431400616 - 1)

Monthly payment = $881.875 * 4.46774431400616 / 3.46774431400616

Monthly payment = $1,136.18

 

Monthly payment if interest rate is 5% = $1,136.18.

 

c)

Calculation of monthly payments be if the interest rate is 6%:

 

Formula;

Monthly payment = P * r * (1 + r)^n / [(1 + r)^n - 1]

Where;

P = Principal loan amount i.e. $211,650

r = Monthly interest rate i.e. 0.005 (0.06 / 12)

n = Monthly period of loan i.e. 360 (30 Years * 12)

 

Now put values in the formula;

Monthly payment = $211650 * 0.005 * (1 + 0.005)^360 / [(1 + 0.005)^360 - 1]

Monthly payment = $1058.25 * 1.005^360 / (1.005^360 - 1)

Monthly payment = $1058.25 * 6.02257521226289 / (6.02257521226289 - 1)

Monthly payment = $1058.25 * 6.02257521226289 / 5.02257521226289

Monthly payment = $1,268.95

 

Monthly payment if interest rate is 6% = $1,268.95.

a) Loan amount = $211,650.

b) Monthly payment if interest rate is 5% = $1,136.18.

c) Monthly payment if interest rate is 6% = $1,268.95.