Question

Your classmate tells you the details of the great deal he got on his mortgage: 30-year 3.5% fixed ratewith a 10% down payment.2. If his new home costs $136,000, what is his down payment?3. How much is he going to borrow to buy the house (assuming he only has the money to make the down paymentfrom the previous question)?4. Determine how much his monthly payments would be. (round to the hundredths places)5. How much will he pay in interest over the lifetime of this mortgage? (round to the hundredths places)

Answer 1

Annuities

The new home costs $136,000.

2. The down payment is 10%:

DP = 10 * $136,000 / 100 = $13,600

The down payment is $13,600

3. Once he pays the down payment, the amount to borrow is:

$136,000 - $13,600 = $122,400.

He is going to borrow $122,400.

4. Now we need to use the annuities formula for A = $122,400, t = 30 years, r = 3.5%, monthly payments.

The formula is:

`A=R*(1-\left(1+i\right)^(-n))/(i)`

Where:

R = Amount of the monthly payments

i = Monthly rate of interest

n = Number of payments

Solving for R:

`R=(A* i)/(1-\left(1+i\right)^(-n))`

Calculate:

`i=(3.5)/(100*12)=0.0029167`

I will keep all the decimals in the calculator. Only a few are shown.

n = 10 years * 12 months per year = 120 payments.

Calculate the amount of the monthly payments:

`\begin{gathered} R=(122,400*0.002916)/(1-\left(1+0.002916\right)^(-120)) \\ Calculating: \\ R=1210.36 \end{gathered}`

The monthly payments would be $1,210.36

5. The final value of the mortgage is given by:

`FV=A\left(1+n\right)^n`

Substituting:

`\begin{gathered} FV=122,400\left(1+0.002916\right)^(120) \\ FV=173,605.41 \end{gathered}`

The interest paid is:

I = FV - A

I = $173,605.41 - $122,400

I = $51,205.41

He would pay $51,205.41 in interest over the lifetime of the mortgage