Question

1. Becca needs to borrow $143,000 to purchase a new home.  The bank has given her two options; the first is a 20 year loan at 4.35% or the second is a 30 year loan at 4.95%.
   1. How much is the payment for each of these loans?

20-year payment______________    30-year payment ______________

2. What is the total cost of each mortgage?

20-year total cost______________   30-year total cost ______________

3. How much will Becca save if she chooses the 20 year loan? _______________

Answer 1

Well looking at the problem logically, the greater the tenure, the higher the interest component of the loan outstanding.

To calculate the payment amount involves simply equating two cash flows together.

a)

We'll denote the yearly payment as 'X' and try to find the same using equations of value.

a_n represents the annuity value. We would assume the same to be the end of the period (Since loans are generally paid at the end of the time period)

20-year payment

Now let us calculate v which is the discount rate.

v = 1 / (1 + 4.35%) = 0.9583133684

Now

Hence the yearly payment is $10,850.866 while the monthly payment is $904.2389

Hopefully now you are clear of the concept! Let me know in comments if you face any more difficulty! Here to help.

30-year payment

Same logic as above

Hence the yearly payment is $9,249 while the monthly payment is $770.78

b) Total cost of each mortgage is simply found by multiplying the the yearly installment by tenure

For 20-year payment it is 10,850.866 * 20 = $217,017.324

For 30-year payment it is 9,249.4029 * 30 = $277,482.089

c)

Money saved = $277,482.089 - $217,017.324 = $60,464.765

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