a A 154700 loan is taken out at 43 for 15 years for the purc

a. A $154,700 loan is taken out at 4.3% for 15 years, for the purchase of a house. The loan requires monthly payments. Find the amount of each payment.

b. In a travel agency marketing survey customers are asked to give their first three choices, in order of preference, of 17 different resorts. In how many different ways can they state their choices?

Solution

a. T = Time Period in months = 15 * 12 = 180

P = Loan Amount = 154700

r = Rate of Interest = (4.3/100)/12 = 43/12000

m = Monthly Payment

=> m = ( r + ( r / ( (1 + r)^t - 1 ) ) * P

Plugging the values

=> m = ( (43/12000) + ( (43/12000) / ( (1 + (43/12000))¹⁸⁰ - 1 ) ) * (154700)

=> m = 1167.6933

b. The ways to select any 3 resorts out of 17 different resorts => ¹⁷C₃

The ways to arrange the selected 3 resorts according to choice => 3!

Total ways to state the choice => 3! * ¹⁷C₃