Question

Question 19 (1 point) A loan of $47,000 calls for payments of $2,700 at the end of every three months until the debt is settled. At an interest rate of 14% compounded semi-annually, how many payments will be made? O24 O40 0 0 27 0 O 14 0

Answer 1

Given interest rate = 14% compounded semiannual

So, Effective annual rate = (1+APR/n)^n - 1 = (1+0.14/2)^2 - 1 = 14.49%

So, quarterly compounded APR = n * ((1+EAR)^(1/n) - 1) = 4*((1.1449^(1/4)) - 1) = 13.76%

Given for loan

Loan amount PV = $47000

payment after every 3 month = $2700

so let assume x payments will be made,

using ordinary annuity formula.

PV = PMT*(1 - (1+r/n)^(-x))/(r/n)

So, 47000 = 2700*(1 - (1+0.1376/4)^(-x))/(0.1376/4)

=> (1 - 1.0344^(-x)) =  0.599

=> 1.0344^x = 2.4935

So, x = 27 periods or payments

So, option C is correct.