Question

Q3 - Time Value of Money Question (20 min) Mortgages are annuities in that a fixed monthly payment is made to the lender (assume end of month payments and an interest rate that compounds semi-annually). Sara is planning to take on a mortgage of $100 000 and believes she can afford monthly payments up to $700. How much interest would she save if she decided to pay off her mortgage over 20 years, rather than over 25 years? Her mortgage is at five percent interest calculated semi-annually.

Answer 1

If her monthly payments are for 700 and the time of mortgage is 25 years then the total amount she pays is calculated as follows:

700 x 25 x 12 = 210,000

So the amount she would pay in interest is the difference of the total amount she pays and the amount of loan

Interest = 210,000 – 100,000 = 110,000

If her monthly payments are for 700 and the time of mortgage is 20 years then the total amount she pays is calculated as follows:

700 x 20 x 12 = 168,000

So the amount she would pay in interest is the difference of the total amount she pays and the amount of loan

Interest = 168,000 – 100,000 = 68,000

Therefore the difference in interest = 110000-68000 = 42000