Question

The price of a small cabin is

​$55 comma 00055,000.

The bank requires a​ 5% down payment. The buyer is offered two mortgage​ options: 20-year fixed at

9.59.5​%

or​ 30-year fixed at

9.59.5​%.

Calculate the amount of interest paid for each option. How much does the buyer save in interest with the​ 20-year option?

Answer 1

Step 1: Price of the small cabin = $55,000

Down payment = 5% of Price of the small cabin = 5% *$55,000 = $2,750

Therefore, loan amount = Price of the small cabin - Down payment

= $55,000 - $22,750 = $52,250

The buyer is offered two mortgage options: 20-year fixed at 9.5%

We can use Present value (PV) of an Annuity formula to calculate the annual payment of loan

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

Where PV (principal amount) = $52,250

PMT = Annual payment =?

n = N = number of payments = 20 years

i = I/Y = interest rate per year = 9.5%

Therefore,

$52,250 = PMT* [1- (1+9.5%)^-20]/9.5%

= $5,929.16

Annual payment is $5,929.16

Total payment = number of payments * Annual payment = 20 *$5,929.16

=$118,583.15

Therefore total interest payment = Total payment - principal payment

= $118,583.15 - $52,250

= $66,333.15

Sep 2: The buyer is offered two mortgage options: 30-year fixed at 9.5%

We can use Present value (PV) of an Annuity formula to calculate the annual payment of loan

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

Where PV (principal amount) = $52,250

PMT = Annual payment =?

n = N = number of payments = 30 years

i = I/Y = interest rate per year = 9.5%

Therefore,

$52,250 = PMT* [1- (1+9.5%)^-30]/9.5%

= $5,312.81

Annual payment is $5,312.81

Total payment = number of payments * Annual payment = 30 * $5,312.81

= $159,384.32

Therefore total interest payment = Total payment - principal payment

= $159,384.32 - $52,250

= $107,134.32

The buyer save in interest with the 20-year option = Total interest payment in 30 years option - Total interest payment in 20 years option

= $107,134.32 - $66,333.15

= $40,801.17

Therefore the buyer saving in interest with the 20-year option is $40,801.17