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?

Answer 1

Here Payments are Done Monthly of $1500 from the beginning of Six Months to Next 01 Year.

Monthly Effective Interest Rate = Annual Rate / 12 = 02% / 12 = 0.001667

Payments are made at Begining in each Month So we will use the formula for Annuity Due.

Future Value of Annuity Due After 01 Year FV1

Here r =  0.001667

PMT = 1500

n = 1500

FV1 = 1.001667 * 1500 *  12.1106 = 18196.196

Now 18196.196 Amount Will Be Invested for the remaining 06 Months.

Semi-Annual Compound Rate = Annual Rate / 2 = 2% / 02 = 01%

After 06 Months This Value Will Be

FV2 = FV1 * ( 1 + Semi-Annual Compound Rate) =  18196.196 * (1 + 01%) = 18377.24  

He will have $ 18377.24 in his TFSA in 2 years’ time if no further contributions are made. (Ans)