Question

Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)

P = 180,000, r = 5.5, t = 28, m = 4

Answer 1

This question requires application of PV of annuity formula according to which

PV =

[1-(4+5)-) [1-(1+r)-n LT P= Periodic Payment r=rate per period n = number of periods

PV = $180,000, n = 28 * 4 = 112 periods, r = 5.5%/4 = 1.375%,

,1- (1 + 0.01375)-112 180,000 = P*9 0,01375

180,000 = P * 56.9715

P = $3,159.48

Answer 2

SOLUTION :

Following formula will be applicable for periodic payment $R to accumulate $P in t years at interest rate of r% per year compounded m times a year ;

P = R((1 + r / (100m))^(mt) - 1) / (r / (100m))   

For P = $180000 ; r = 5.5% ; t = 28 years ; m = 4 , we have :

=> 180000 = R ( (1 + 5.5 / 400)^(112) - 1 ) / (5.5/ 400)

=> 180000 = R * 262.975115116

=> R = 180000/262.975115116

=> R = 684.48 ($) (ANSWER).

Answer 3

SOLUTION :

Following formula will be applicable for periodic payment $R to pay the loan  $P in t years at interest rate of r% per year compounded m times a year ;

PV = P = R((1 + r / (100m))^(mt) - 1) / (r / (100m))   

For P = $180000 ; r = 5.5% ; t = 28 years ; m = 4 , we have :

=> 180000 = R ( (1 + 5.5 / 400)^(112) - 1 ) / ( (5.5/ 400) *(1 + 5.5 / 400)^(112) )

=> 180000 = R * 56.9714831

=> R = 180000/56.9714831

=> R = 3159.48 ($) (ANSWER).