Question

You are applying for an 80/20 mortgage to buy a house costing $175,000.

The first (80%) mortgage has an interest rate of 4.75%, and the second (20%)
mortgage has an interest rate of 7.525%. Both the first mortgage and the
second mortgage are 30-year fixed-rate mortgages. What will the total
amount of the mortgage be?

Answer 1

Answer:351,226.80

Explanation:

Answer 2

The total amount of the mortgage is $ 871879.4

Explanation:

Given as :

The cost of house = $ 175,000

The first 80% of mortgage amount = 80% of $ 175,000 = 140,000

The second 20 % of mortgage amount = 20% of $ 175,000 = 35,000

The rate of interest for 80 % mortgage = 4.75 %

The rate of interest for 20 % mortgage = 7.525 %

The time period for both mortgage is 30 years

Let The amount at 80 % mortgage =
`A_1`

And The amount at 20 % mortgage =
`A_2`

So, From compounded method

`A_1` = principal ×
`(1+(\textrm rate)/(100))^(\textrm time)`

or,
`A_1` = 140,000 ×
`(1+(\textrm 4.75)/(100))^(\textrm 30)`

Or,
`A_1` = 140,000 ×
`(1.0475)^(30)`

Or,
`A_1` = 140,000 × 4.02365

Or,
`A_1` = $ 563311

Again

`A_2` = principal ×
`(1+(\textrm rate)/(100))^(\textrm time)`

or,
`A_2` = 35,000 ×
`(1+(\textrm 7.525)/(100))^(\textrm 30)`

Or,
`A_2` = 35,000 ×
`(1.07525)^(30)`

Or,
`A_2` = 35,000 × 8.81624

Or,
`A_2` = $ 308568.4

∴ Total amount A =
`A_1` +
`A_2`

I.e A = $ 563311 + $ 308568.4 = $ 871879.4

Hence The total amount of the mortgage is $ 871879.4 answer