Question

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.

Answer 1

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