Question

Ricardo is aware that he should save as much as possible early in his career while his personal responsibilities are minimal.  Therefore he has adopted an aggressive savings plan – put aside $1,500 in his TFSA at the beginning of each month for a year.  (He has never contributed to a TFSA and has sufficient contribution room.)  Ricardo’s savings are expected to earn 2% per annum, compounded semi-annually and he will make his first contribution 6 months from today.  How much will he have in his TFSA in 2 years’ time if no further contributions are made?

1. $18,195
2. $18,377
3. $18,407
4. $18,502

Answer 1

Select - (b) .......... 18377

Annual Interest rate = 0.02

Semi annual rate = 0.02 / 2 = 0.01

Equivalent monthly rate = x .......so, ( 1 + x )6 - 1 = 0.01

( 1 + x )6 = 1.01

1 + x = 6th Root ( 1.01 ) = 1.0016597644

Future value of annuity (immediate ) = [ ( 1 + r )n - 1 ] / r * ( 1 + r )

= [ ( 1.0016597644 )12 - 1 ] / 0.0016597644 * ( 1.0016597644 )

= 12.130253

Future value of savings by the end of 3rd half year = 1500 * 12.130253 = 18195.38

Future value after the end of 2 years = 18195.38 * 1.01 = 18377.33