Question

Jim and Susie take out a mortage for $110,000 at 9.5% for 30 years.
What are their monthly payments?
$  

After 3 years, they decide to refinance. How much do they still owe?
$  

They refinance with a 9% 15 year loan. What are their new monthly payments?
$  

How much will they save by refinancing?
$

Answer 1

Jim and Susie take out a mortage for $110,000 at 9.5% for 30 years.

1. What are their monthly payments?

Monthly payment (PMT) on loan can be calculated with the help of PV of an Annuity formula

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

Where,

Present value (PV) =$110,000

PMT = Monthly payment =?

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

i = I/Y = interest rate per year = 9.5%; therefore monthly interest rate = 9.5%/12 = 0.79% per month

Therefore,

$110,000 = PMT* [1- (1+0.79%) ^-360]/0.79%

= $924.94

2. After 3 years, they decide to refinance. How much do they still owe?

The loan balance After 3 years (36 months) is the present value of loan calculated for 360 - 36 = 324 payments (months)

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

Where,

Present value (PV) =?

PMT = Monthly payment = $924.94

n = N = number of payments = 360 - 36 = 324 months

i = I/Y = interest rate per year = 9.5%; therefore monthly interest rate = 9.5%/12 = 0.79% per month

Therefore,

PV of loan (balance amount after 3 years) = $924.94* [1- (1+0.79%) ^-324]/0.79%

= $107,756.44

3. They refinance with a 9% 15 year loan. What are their new monthly payments?

Monthly payment (PMT) after refinancing the loan can be calculated with the help of PV of an Annuity formula

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

Where,

Present value (PV) = $107,756.44

PMT = Monthly payment =?

n = N = number of payments = 12 *15 years = 180 payments

i = I/Y = interest rate per year = 9.0%; therefore monthly interest rate = 9.0%/12 = 0.75% per month

Therefore,

$107,756.44 = PMT* [1- (1+0.75%) ^-180]/0.75%

= $1,090.61

4. How much will they save by refinancing?

Saving by refinancing = PMT in part 1 * months remaining for loan at time of refinancing – PMT in part 3 * months of refinanced loan

= $924.94* 324 - $1,090.61 * 180

= $299,680.44 - $196,310.51

= $103,369.93

Therefore money saved through refinancing is $103,369.93