Question

What is the amount of interest earned in the 33rd semi-annual deposit interval of a sinking fund that is set up to pay back a debt of $220000 over 19 years? The fund earns 4.62% compounded semi-annually and the deposits are made semi-annually.

Answer 1

Step-1:Calculation of semi annual payment
Semi annual payment	=	Future value of semi annual payment	/	Future value of annuity of 1
	=	$ 2,20,000.00	/	59.81389
	=	$       3,678.08
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.0231)^38)-1)/0.0231		i	=	4.62%/2	=	0.0231
	=	59.81389095		n	=	19*2	=	38
Step-2:Calculation of future value of semi annual payment after 32nd semi annual payment
Future value	=	Semi annual payment	*	Future value of annuity of 1
	=	$       3,678.08	*	46.61141
	=	$ 1,71,440.29
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.0231)^32)-1)/0.0231		i	=	4.62%/2	=	0.0231
	=	46.61141354		n			=	32
Step-3:Calculation of interest earned in 33rd semi annual deposit
Interest earned	=	Investment value at the beginning of 33rd payment	*	Semi annual interest rate
	=	$ 1,71,440.29	*	0.0231
	=	$       3,960.27