Question

Assume that one of your cousins takes a loan of $12,000 from a bank at 18 per cent interest rate. If your cousin plans to repay $1,200 per quarter against this loan amount, in how many years she would be able to repay the loan (and accumulated interest) fully?

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	$     12,000
PMT = the dollar amount of each annuity payment	$       4,800	1200*4
r = the effective interest rate (also known as the discount rate)	19.25%	((1+18%/4)^4)-1)
i=nominal Interest rate	18%
n = the number of periods in which payments will be made	To be computed
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / i)
12000=	4800* (((1-(1 + 19.25%) ^- n)) / 18%)
((1-(1 + 19.25%) ^- n)) / 18%=	12000/4800
((1-(1 + 19.25%) ^- n)) / 18%=	2.50
((1-(1 + 19.25%) ^- n))=	2.50*18%
((1-(1 + 19.25%) ^- n))=	0.45
-(1 + 19.25%) ^- n=	0.45-1
-(1 + 19.25%) ^- n=	-0.55
1.1925^-n=	0.55
-n Log 1.1925	log 0.55
-n * 0.07645839=	-0.25963731
N=	0.25963731/0.07645839
N=	3.40	Years