Question

If Paige has accumulated $6200 by saving $80 every month for six ​years, what nominal annual rate of interest compounded semi-annually has been​ earned?

The nominal annual rate of interest is _____%compounded semi-annually

Answer 1

0.4104%

Step-1:Calculation of effective annual interest on monthly saving
Effective annual interest	=	((1+(i/n))^n)-1	Where,
	=	((1+(0.004100/12))^12)-1	i	=	0.4100%
	=	0.4108%		n	=	12
Working:
Nominal annual rate of interest	=rate(nper,pmt,pv,fv)*2
	= 0.4100%
Where,
nper	=	Number of period	=	6*12	=	72
pmt	=	Periodic cash flow		=	$     -80.00
pv	=	Initial cash flow		=	0
fv	=	Future cash flow		=	$ 6,200.00
Step-2:Calculation of nominal interest rate with semi annual compounding
Effective annual rate	=	((1+(I/n))^n)-1	Where,
0.004108		=	((1+(i/2))^2)-1	i	=	Nominal annual rate
1.004108		=	(1+(i/2))^2	n	=	Number of times compounding
1.004108	^(1/2)	=	1+(i/2)
1.002052		=	1+(i/2)
0.002052		=	i/2
0.004104		=	i
So,
Nominal annual rate with semi annual compounding	=	0.4104%
Note:
Effective annual interest rate must be same for both monthly and semi annually compounding.