Question

Cynthia has the choice of taking out a 25-year loan for $155,000 at 4.4% interest, compounded monthly, or the same loan at 20 years for a higher monthly payment. If she would pay a total of $100,831 in interest on the 25- year loan, how much in total would she pay in interest on the 20-year loan?

Answer 1

Answer: Less than $100,831

Step-by-step explanation:

There is an equation for the calculation monthly payment which is:

x = p × r × (1+r)^n / (1+r)^n - 1

where,

p= the amount of loan, which is $155,000.

r = monthly interest rate, which is (4.4/12)/100 = 0.00367

n = number of months for paying back, which is 20 × 12 = 240

Since we have all the values, we plug them in and solve.

x = 155,000 × 0.00367 × (1.00367^240) / (1.00367^240) - 1

x = $972.27

Therefore, the monthly payment is approximately $972.3. We csn now multiply it by the number of months in order to get total payment:

$973.3 × 240 = $233,352

Therefore, the total amount, which is the loan plus the interest, will be 233,352 dollars.

To find the amount of interest, we subtract the loan from total amount:

= $233,352 - $155,000

= $78,352