Question

18. The interest rates that the Global Bank pays for different compounding frequencies are presented below. Assume that your investment horizon is 1 year. (1 year = 360 days = 52 weeks) Compounding frequency Annual interest rate Daily 10.80% Weekly 10.60% Monthly 11.00% Quarterly 11.20%

Answer 1

Answer:

In order to determine which alternative will give you the largest fund of money at the end of one year we need to find out the effective rate of interest.The effective rate of interest is defined as the annual rate of interest that is actually being earned on your investment.

The formula for determining the effective rate of interest is:

Effective Rate of Interest= (1+r/n)^n-1

where: r= given interest rate, n=number of compounding periods

Here: For Daily: n=365(1 year has 365 days) r= 10.80% or 0.108 .Putting these values into the formula for effective interest rate we get:Effective Rate of Interest= (1+0.108/365)^365-1ie. 0.1140 or 11.40%

Here: For Weekly: n=52 r= 10.60% or 0.106 .Putting these values into the formula for effective interest rate we get:Effective Rate of Interest= (1+0.106/52)^52-1ie. 0.1117 or 11.17%

Here: For Monthly: n=12 r= 11.00% or 0.11 .Putting these values into the formula for effective interest rate we get:Effective Rate of Interest= (1+0.11/12)^12-1ie.0.1157or 11.57%

Here: For Quarterly: n=4 r= 11.20% or 0.112 .Putting these values into the formula for effective interest rate we get:Effective Rate of Interest= (1+0.112/4)^4-1ie. 0.1168 or 11.68%

From the above options we find that the quarterly option has the highest effective interest rate and hence you should go with the quarterly alternative