Series and sequence question- confused if answer is correct (1 Viewer)

[parasdeep1807]

Hi guys just needed help with a loan repayment question.
Just made it up so i dont have the answer but wanted to check if its correct.

Question: Chris takes a loan of 250,000 at 6%pa compounded monthly (at the start of each month). He makes repayment at the end of every year. What repayments will he need to make to pay off the loan completely in 20 years.

R is for repayment
So I did:
M1: 250,000 x 1.005^1
M2: 250,000 x 1.005^2
M12: 250,000 x 1.005^12 - R
M13: 250,000 x 1.005^13 - R x 1.005
M25: 250,000 x 1.005^25 - R x 1.005^13 - R x 1.005

n = number of years
Mn: 250,000 x 1.005^(12n) -R [1 + 1.005^12(2) + 1.005^12(3)+...+ 1.005^12(n-2) + 1.005^12(n-1)]

The GP becomes: [1.005^12(20) - 1] / [1.005^12 - 1]

The repayment answer I got was $22093.95

My teacher got an answer around $39000 so Im very confused.

Thanks for the help

Edit: M stands for month and Mn = 240 months (20 years)

 

[ichila101]

No idea cause I got the same answer as you, show your teacher your working and ask them where you went wrong? I am pretty sure your answer is right though...