Question

Suppose you want to buy a condominium that costs $320,000. You will make a down payment equal to 20 percent of the price of the condominium and finance the remainder with a loan that has an interest rate of 4.65 percent compounded monthly. If the loan is for 30 years, what are your monthly mortgage payments? Multiple Choice $1,350.89 $1,286.48 $1,320.03 $1,468.12 $1,534.46

Answer 1

Answer: c. $ 1320.03

Explanatory Solution:

Given:

Condominium Costs = $ 320,000

Down Payment Amount = 20 % of Condominium Costs i.e. 20 % of $ 320,000 = $ 64,000

Loan Amount = Remaining of Down Payment Amount i.e. 80 % of $ 320,000 = $ 256,000

Interest Rate on Loan = 4.65 % Compounded Monthly

Loan Duration = 30 Years

To Calculate:

Monthly Mortgage Payments on loan

Formula:

M = P [ i (1 + i) ^n] / [ (1 + i) ^n – 1]

Where:

M = Monthly Mortgage Payment

P = Principal Amount

i= Interest Rate Per Month

n= Total Number of Months in Loan Duration

Here:

Principal Amount = $ 256,000

Interest Rate = 4.65 Per Year

Interest Rate Per Month = 0.0465 / 12 = 0.003875

Loan Repayment Duration in Years = 30 Years

Number of Months Required to Repay Loan = 30 Years × 12 Months = 360 Months

On putting the above values in the following formula, we get

M = P × [ i (1 + i) ^n] / [ (1 + i) ^n – 1]

M = $ 256,000 ((0.003875 (1 +0.003875) ^ 360) / (1 + 0.003875) ^ 360 – 1))

M = $ 256,000 × ((0.003875 × (1.003875) ^ 360) / (1.003875) ^ 360 – 1))

M = $ 256,000 × ((0.003875 × 4.024) / (4.024 – 1))

M= $ 256,000 × ((0.015593) / (3.024))

M = $ 256,000 × 0.0051564

M = $ 1320.0384 ≈ $ 1320.03

Monthly Mortgage Payments on Loan= $ 1320.03

So, our answer option is 'c'

Ans: c. $ 1320.03