Question

Leila is considering buying her first home. The house she is interested in buying is priced at $125,000. Leila can put down a $20,000 payment, and she qualifies for a 30-year mortgage at 6%. What will her monthly mortgage payment be?

Answer 1

* The monthly mortgage payment is $629.53 ⇒ answer C

Explanation:

* Lets explain how to solve the problem

- Leila is considering buying her first home

- The house she is interested in buying is priced at $125,000

∴ She can put $20000 down payment

* Lets find the balance to be paid off on mortgage

∴ The balance = 125000 - 20000 = 105000

- She qualifies for a 30-year mortgage at 6%

* Lets find the rule of the monthly payment

∵
`pmt=((r)/(n)[P(1+(r)/(n))^(tn)])/((1+(r)/(n))^(tn)-1)` , where

- pmt is the monthly mortgage payment

- P = the initial amount

- r = the annual interest rate (decimal)

- n = the number of times that interest is compounded per unit t

- t = the time the money is invested or borrowed for

∵ P = 105000

∵ r = 6/100 = 0.06

∵ n = 12

∵ t = 30

∴
`pmt=((0.06)/(12)[105000(1+(0.06)/(12))^(30(12)))/((1+(0.06)/(12))^(30(12))-1)`

∴
`pmt=(0.005[105000(1.005)^(360)])/((1.005)^(360)-1) =629.528`

* The monthly mortgage payment is $629.53