Question

If Gayle contributes $1,900 to her RRSP at the end of every quarter for the next 11 years and then contributes $1,900 at each month’s end for the subsequent 10 years, how much will she have in her RRSP at the end of the 21 years? Assume that the RRSP earns 9.4% compounded semiannually. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Gayle will have

$

please I need steps for the answer

Answer 1

$ 730,302.73

Step-1:Calculation of future value of Quarterly deposit in 21 years
Future Value	=	Quarterly deposit of 11 years	*	Future Value of annuity of 1 for 11 years	*	Future Value of 1 for 10 years
	=	1,900.00	*	75.19527537	*	2.505726313
	=	3,57,995.68
Working:
Deposits are made quarterly and interest rate compounds semi annually.
So, we need to calculate equivalent quarterly interest rate.
# 1
(1+i)^n	=	(1+i)^n		Where,
(1+i)^2	=	(1+0.047)^1		Semi annual interest rate	=	9.4%/2
1+i	=	1.047	^ (1/2)		=	0.047
1+i	=	1.0232
i	=	0.0232
So, Equivalent quarterly interest rate	=	2.32%
# 2
Future Value of annuity of 1 for 11 years	=	(((1+i)^n)-1)/i		Where,
	=	75.1953		i	=	2.32%
				n	=	44
# 3
Future Value of 1 for 10 years	=	(1+i)^n		Where,
	=	2.5057		i	=	2.32%
				n	=	40
Step-2:Calculation of future value of monthly deposit in 21 years
Future Value	=	Monthly Deposit	*	Future Value of annuity of 1 for 10 years
	=	1,900.00	*	195.9510797
	=	3,72,307.05
Working:
Deposits are made monthly and interest rate compounds semi annually.
So, we need to calculate equivalent monthly interest rate.
# 1
(1+i)^n	=	(1+i)^n		Where,
(1+i)^6	=	(1+0.047)^1		Semi annual interest rate	=	9.4%/2
1+i	=	1.047	^ (1/6)		=	0.047
1+i	=	1.0077
i	=	0.0077
So, Equivalent monthly interest rate	=	0.77%
# 2
Future Value of annuity of 1 for 11 years	=	(((1+i)^n)-1)/i		Where,
	=	195.9511		i	=	0.77%
				n	=	120
Step-3:Calculation of RRSP value
RRSP Value in 21 Years	=	3,57,995.68	+	3,72,307.05
	=	7,30,302.73