Pre Calculus finance unit

Question

Determine which of the following investments will have a 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 annually rate of interest of 9.8% compounded semi-annually.

Even you could just let me know the best formulas to use that would help to thanks.

Answer 1

a) total after 5 years = 40000 (1.065) ^ 5 = 54803.46654

Annual rate of return (%) = [(54803.47 - 40000) / 40000] x (100/5) = 7.4 %

b) total = 10000 + (5 x 10000 x 0.078) = 13900

Annual rate of return = (13900 - 10000) / 10000 x (100/5) = 7.8%

c) This is unclear, as how should the interest be calculated as the capital in the account is increasing month by month because of deposits. You could assume monthly interest of 9.8 / 12 %, and then add interest twice a year, but it's not a straightforward formula, could be modelled on a spreadsheet.

Answer 2

To find compound interest, we use a formula where P=Principal (the original deposited amount), A=present or final amount,

r=percent rate written as a decimal (divide the percent by 100),

t=number of time periods, usually years,

1=the decimal form of 100%, to which we're adding each time we compound,

k=the number of times per time period that the compounding takes place (sometimes this is n instead of k)

And we get...

A=P(1+r/k)^kt

So the Final Amount equals the initial investment times 100% plus the rate, divided, if necessary, by the number of times this is done per year, and multiplied by itself the total number of times the compounding happens.

A. A five year $40000 GIC that earns an annual rate of interest of 6.5% compounded annually.

A=40,000(1+.065)⁵=$54,803.47.

B. A five year $10000 CSB that pays simple interest of 7.8% per year.

Simple Interest does not grow exponentially, or compound on previous values, like compound interest. The formula is just A=P(1+rt)

A=10,000(1+.078·5)=$13,900

C. This is a more complicated formula. I can't write it well here, but you can see it at https://www.bizskinny.com/Finance/Compound-Interest/compound-interest-with-monthly-contributions.php.

A=$86,331.97.

I hope this helps, and if you don't understand where the formulas come from, check out Eddie Woo's videos on compound interest. He's great!

Have fun mathing, and get in touch if you have more questions!

Liz Z.