Question

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Sophie invested $2,100 at the beginning of every 6 months in an RRSP for 11 years....

Sophie invested $2,100 at the beginning of every 6 months in an RRSP for 11 years. For the first 9 years it earned interest at a rate of 3.70% compounded semi-annually and for the next 2 years it earned interest at a rate of 5.50% compounded semi-annually.

a. Calculate the accumulated value of her investment at the end of the first 9 years.

b. Calculate the accumulated value of her investment at the end of 11 years.

c. Calculate the amount of interest earned from the investment.

Expert Solution

The future value needs to be calculated using FV function in EXCEL

=FV(rate,nper,pmt,pv,type)

a. Here the compunding is semi-annual (2 periods in a year)

rate=3.7%/2=1.85%

nper=number of periods=2*9=18

pmt=2100

pv=0

type=1 (because payments are deposited at the begining of 6 months)

=FV(1.85%,18,-2100,0,1)

FV=$45,194.32

The accumulated value of her investment at the end of the first 9 years=$45,194.32

b. Use the same formula to find the accumulated value for next two years.

rate=5.5%/2=2.75%

nper=2*2=4

=FV(2.75%,4,-2100,0,1)

FV=$8,993.60

*Please remember that the 9 years amount $45,194.32 will earn the interest for next two years. The value becomes=$45194.32*((1+2.75%)^4)=$50,374.55

The total accumulated value of her investment at the end of 11 years=$8,993.60+$50,374.55=$59,368.15

c. The total investment made for 11 years=2100*22=$46,200 (total 22 periods with semi-annual payments)

The total interest earned=Total accumulated amount as after 11 years-Total investment=$59,368.15-$46,200=$13,168.15

jeff jeffy answered 2 years ago

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