## Tom wishes to purchase a property that has been valued at \$300,000. He has \$30,000 available as a deposit, and will require a mortgage for t

Question

Tom wishes to purchase a property that has been valued at \$300,000. He has \$30,000 available as a deposit, and will require a mortgage for the remaining amount. The bank offers him a 25-year mortgage at 2% interest, compounded monthly. Calculate the total interest paid on the mortgage. Round your answer to the nearest dollar.

in progress 0
7 days 2021-10-07T13:13:26+00:00 2 Answers 0

Step-by-step explanation:

First we note that Tom requires a mortgage on \$300,000−\$30,000=\$270,000. To calculate the monthly payments we must apply the loan formula and solve for d.

P=d(1−(1+rn)−nt(rn).

We have P=\$270,000,r=0.02,n=12,t=25, so substituting in the numbers into the formula gives

\$270,000=d(1−(1+0.0212)−25⋅12)(0.0212),

that is,

\$270,000=235.9301d⟹d=\$1,144.41.

So our monthly repayments are d=\$1,144.41. To calculate the total interest paid, we find out the entire amount that’s paid over the lifetime of the mortgage and subtract the principal. The total amount paid is

\$1,144.41×12×25=\$343,323

and therefore the total amount of interest paid is

\$343,323−\$270,000=\$73,323.

2. Answer: The total interest paid on the mortgage is \$179550

Step-by-step explanation:

The initial cost of the property is \$300000. If he deposits \$30000, the remaining amount would be

300000 – 30000 = \$270000

Since the remaining amount was compounded, we would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 270000

r = 2% = 2/100 = 0.02

n = 12 because it was compounded 12 times in a year.

t = 25 years

Therefore,

A = 270000(1+0.02/12)^12 × 25

A = 270000(1+0.0017)^300

A = 270000(1.0017)^300

A = \$449550

The total interest paid on the mortgage is

449550 – 270000 = \$179550