Question

Annual contributions to a TFSA of $2000 will be made for 30 years.  The contributor expects investments within the plan to earn 8% compounded annually.  What will the TFSA account be worth after 30 years if the contributions are made:

a) At the end of the year?

b) At the beginning of the year?

c) What is the accumulated interest for end of year contributions vs beginning of year contributions?

Show workings

Answer 1

(a) Here, the deposits will be same every year, so it is an annuity. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $2000, r is the rate of interest = 8% and n is the time period = 30

Now, putting these values in the above formula, we get,

FVA = $2000 * ((1 + 8%)30 - 1 / 8%)

FVA = $2000 * ((1 + 0.08)30 - 1 / 0.08)

FVA = $2000 * ((1.08)30 - 1 / 0.08)

FVA = $2000 * ((10.0626568891 - 1 / 0.08)

FVA = $2000 * (9.0626568891 / 0.08)

FVA = $2000 * 113.283211113

FVA = $226566.42

So, TFSA account will be worth $226566.42

(b) Here, the deposits will be same every year, so it is an annuity. And the deposits start at the beginning of each year, so it is an annuity due. We need to calculate the future value of annuity due by the following formula:

FVAD = (1 + r) * P * ((1 + r)n  - 1 / r)

where, FVAD is future value of annuity due, P is the periodical amount = $2000, r is the rate of interest = 8% and n is the time period = 30

Now, putting these values in the above formula, we get,

FVAD = (1 + 8%) * $2000 * ((1 + 8%)30 - 1 / 8%)

FVAD = (1 + 0.08) * $2000 * ((1 + 0.08)730 - 1 / 0.08)

FVAD = (1.08) * $2000 * ((1.08)30 - 1 / 0.08)

FVAD = (1.08) * $2000 * ((10.0626568891- 1) / 0.08)

FVAD = (1.08) * $2000 * (9.0626568891 / 0.08)

FVAD = (1.08) * $2000 * 113.283211113

FVAD = $244691.74

So, TFSA account will be worth $244691.74.

(c) Calculation of accumulated interest for end of year contributions:

Total contributions = $2000 * 30 = $60000

Future value = $225566.42

Interest = Future value - Total contributions

Interest = $226566.42 - $60000 = $166566.42

Calculation of accumulated interest for beginning of year contributions:

Total contributions = $2000 * 30 = $60000

Future value = $244691.74

Interest = Future value - Total contributions

Interest = $244691.74 - $60000 = $184691.74