Question

RBC is offering a one year Term Deposit that pays 8% compounded quarterly. CIBC is offering a 18-month GIC that pays 8.05% compounded semi-annually. Find the effective rate of interest for both investment options. Explain which option would you choose to invest an amount.  

Answer 1

The effective rate of interest is the actual rate of interest after the compounding of interest for the given period.

Normally the interest rate are on annual basis, but when they stands compounded there comes the concept of effective interest rate.

To compare the two investment or rates the tenure and effective interest rate for equal period is to be taken, here the effective rate is to be taken on basis of 1 year.

1. For RBC 1 year term deposit, the rate of interest is 8% which is compounded quarterly. So the interest rate is to be reduced to 2% for each quarter and for 1 year time period will be 4 quarter i.e 4 period.

Let the amount be 100, so interest calculation will be as follows : A = amount after the period, P is the principal amount i.e 100 , r = rate of interest quarterly i.e 2% , n is period = 4

A = P × ( 1 + r )^n

i.e A = 100 × ( 1 + 2/100) ^4.

A = 100 ×( 1.02)^4. = 100 × 1.0824 = 108.24.

Interest = A - P i.e Interest = 108.24 - 100 = 8.24. which is the effective interest rate for 1 year

So the effective interest rate = 8.24 %.

2.

For CIBC, the interest rate is compounded semi annually at an interst rate of 8.05 % ,

Here the interest will be for 2 period , and rate of interest will be , 4.025 % ( 8.05/2).

So Let P be 100, r = 4.025 and n = 2 ,

A = P × ( 1+ r )^n.

A = 100 × ( 1 + 4.025 /100)^2

A = 100 × (1.04025)^2 = 100 × 1.0821.

A = 108.21

Interest = A - P = 108.21 - 100 = 8.21 , so effective interest rate will be 8.21%.

So effective interest rate = 8.21%.

Now for the option to be chosen for investment should be the option with higher effective interest rate. Here in the given case RBC's effective interest rate is 8.24 % whereas fo CIBC the effective interest rate is 8.21% it clearly shows that effective annual interest rate of RBC is higher so it should be selected.

So RBC's investment option is to be taken