Question

In terms of paying less in? interest, which is more economical for a ?$80 comma 000 ?mortgage: a? 30-year fixed-rate at 7?% or a? 15-year fixed-rate at 6.5?%? How much is saved in? interest?

Answer 1

Formula:

Present value of Annuity = A * [1 - {1/(1+r)^n}] / r

where, A is Annuity

           r is rate of interest

           n is no. of years

Scenario1:

Present value of annuity = 80

r = 7%

n = 30

Substitute the values in above formula:

80 = A * [1 - {1/(1+0.07)^30}] / 0.07

Annuity = $6.446

Scenario 2:

r = 6.5%

n = 15

Substituting the values in above formula:

80 = A * [1 - {1/(1+0.065)^15}] / 0.065

Annuity = $8.508

Based on the above calculations, we can say that Scenario 1 is more economical since annuity amount paid is lesser than scenario 2.

Interest saved = (8.508 - 6.446) = $2.062