Question

# Ali deposited \$1,400 at the end of every month into an RRSP for 8 years. The...

Ali deposited \$1,400 at the end of every month into an RRSP for 8 years. The interest rate earned was 4.75% compounded semi-annually for the first 4 years and changed to 5.00% compounded monthly for the next 4 years. What was the accumulated value of the RRSP at the end of 8 years?

Solution :-

Interest rate for 6 months = 4.75% / 2 = 2.375%

Interest rate per month = ( 1 + 0.02375 )1/6 - 1 = 0.0039197 = 0.39197%

Value of fund after first fours = \$1,400 * FVAF ( 0.39197% , 48 )

= \$1,400 * 52.6993

= \$73,779.01

After first 4 Years :-

Interest Rate per month = 5.00% / 12 = 0.4167%

Effective annual Interest rate = ( 1 + 0.004167 )12 - 1 = 0.051162 = 5.1162%

Value of \$73,779.01 after next four years

= \$73,779.01 * ( 1 + 0.051162 )4

= \$73,779.01 * 1.22089

= \$90,076.46

Value of annual deposit fund of next 4 years = \$1,400 * FVAF ( 0.4167% , 48 )

= \$1,400 * 53.0149

= \$74,220.84

Now Value of the RRSP at the end of 8 years =  \$90,076.46 + \$74,220.84 = \$164,297.30

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