Question

An executive wishes to take out a $1.2 m mortgage. The yearly interest rate on the loan is 1.95% and the loan is for 20 years. What will the monthly repayments be? Give your answer in dollars and cents. Do not include commas or the dollar sign in your answer.

Answer 1

To find the monthly payment for a $1.2 million mortgage at a 1.95% annual interest rate over 20 years, the formula P = [rPv] / [1 - (1 + r)^(-n)] is used. The resulting monthly payments are approximately $6347.40.

Step-by-step explanation:

To calculate the monthly repayments for a $1.2 million mortgage with a yearly interest rate of 1.95% over 20 years, we can use the formula for an amortizing loan monthly payment:

`P = [rPv] / [1 - (1 + r)^(-n)]`

Where:
P is the monthly payment
r is the monthly interest rate
Pv is the loan principal (initial amount borrowed)
n is the total number of payments (months)

First, we convert the annual interest rate to a monthly rate by dividing by 12 months:

Monthly interest rate = 1.95% / 12
Monthly interest rate = 0.1625%

Now, to convert the percentage to a decimal we divide by 100:

Monthly interest rate (decimal) = 0.001625

Next, we calculate n, the total number of payments:

n = 20 years * 12 months/year
n = 240 months

Now we can use the formula:

P = [0.001625 * 1200000] / [1 - (1 + 0.001625)^(-240)]
P = 6347.4049

Round off to nearest cent:

Monthly payment = $6347.40

Answer 2

Mortgages are calculated using simple interest, so:

`A=P(1+rt)`

P= principal amount

r= interest rate

t= time

For P=1.2mill

r=1.95%

t=20years

The simple interest will be:

`A=1200000(1+0.0195\cdot20)=1668000`

Now divide the calculated amount by 20 to get the yearly fee:

`(1668000)/(20)=83400`

And finally divide it by 12 to get the monthly fee:

`(83400)/(12)=6950`

The exercutive will pay 6950 monthly