Question 1189246: 14.Determine which of the following investments will have the greater rate of return.
a.A five year $40000 GIC that earns an annual rate of interest of 6.5% compounded annually.
b.A five year $10000 CSB that pays simple interest of 7.8% per year.
c.An investment where $2500 is deposited each month into an account for five years that pays an annual rate of interest of 9.8% compounded semi-annually.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a. A five year $40000 GIC that earns an annual rate of interest of 6.5% compounded annually.
40,000 at 6.5% per year, compounded annually for 5 years, gives you a future value of 40,000 * 1.065^5 = 54,803.46654.
that's an overall growth rate of 54,803.46654 / 40,000 = 1.370086664.
that's an annual growth rate of that ^ (1/5) = 1.065 per year.
b. A five year $10000 CSB that pays simple interest of 7.8% per year.
10,000 at 7.8% per year, simple interest for 5 years, give you a future value of 10,000 * .078 * 5 + 10,000 = 13,900.
that's an overall growth rate of 13,900 / 10,000 = 1.39.
that's an annual growth rate of that ^ (1/5) = 1.068077976.
c. An investment where $2500 is deposited each month into an account for five years that pays an annual rate of interest of 9.8% compounded semi-annually.
you can use a formula for this, or you can use an online calculator, such as the one found at https://arachnoid.com/finance/index.html
the results of using that calculator are shown below:
the first use of the calculator found the present value of 60 end of month payments of 2500.
the second use of the calculator found the future value of 60 end of month payment of 2500.
the interest rate used was calculated as follows:
9.8/2 = 4.9% per 6 month period.
1.049^(1/6) = 1.008004756 - 1 = .008004756 * 100 = .8004756% per month.
that's the interest rate that was used.
the display shows that rounded to 6 decimal places, but the interest rate used in the calculation was that.
the overall growth rate was the future value divided by the present value = 191,588.51 / 118,744.77 = 1.613447986.
that's an annual growth of that ^ 1/5) = 1.100401044.
the annual growth rate are:
1.065 for selection (a).
1.068077976 for selection (b).
1.100401044 for selection (c).
the clear winner is selection (c).
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