Grade 11 Math Problems

• Jun 16th 2008, 10:03 AM
VDestinV
Grade 11 Math Problems
I need to get these two questions fully understood so could someone please answer them and explain thank you.

1) Madeleine works at a company that offers bonuses to its employees, depending on their performance. Madeleine is offered the choice of recieving four cheques of $300, one every 3 months throughout the year, or waiting until the end of the year and recieving a single cheque of$1300. Madeleine finds out that the highest interest rate offered by the banks os a guaranteed rate of 7.5% interest compounded quareterly. Illustrate Madeleine's choices using a timeline, to help her decide which bonus offer to accept.

2) Would you make more money by investing $100 a month at 12% interest compounded monthly for 5 years or by investing$1200 a year at 12% interest compounded annually for 5 years?
• Jun 16th 2008, 10:10 AM
VDestinV
Forget about #2 I figured it out :)
• Jun 16th 2008, 10:32 AM
TheEmptySet
Quote:

Originally Posted by VDestinV
I need to get these two questions fully understood so could someone please answer them and explain thank you.

1) Madeleine works at a company that offers bonuses to its employees, depending on their performance. Madeleine is offered the choice of recieving four cheques of $300, one every 3 months throughout the year, or waiting until the end of the year and recieving a single cheque of$1300. Madeleine finds out that the highest interest rate offered by the banks os a guaranteed rate of 7.5% interest compounded quareterly. Illustrate Madeleine's choices using a timeline, to help her decide which bonus offer to accept.

2) Would you make more money by investing $100 a month at 12% interest compounded monthly for 5 years or by investing$1200 a year at 12% interest compounded annually for 5 years?

We will need the formlula

$A=A_0\left( 1+\frac{r}{n}\right)^{nt}$ where r is the interest rate and n is the number times compounded per year and t is time (in years)

I'm guessing this is what you mean at time t=0 she gets 300 then in three months she gets 300 more,... so after nine months the company has given her $1200 dollars we want to know if she can make more money if she takes this option then the$1300 lump sum.

We know that $A_0=300 \\\ r=0.075 \\\ n=4$ so we get

$A=300(1+\frac{0.075}{4})^{4t}$

We need to find out how much money she has after 3 months so (1/4 of a year) so we get

$A=300(1+\frac{0.075}{4})^{4\cdot \frac{1}{4}}=305.625$

But now she gets another 300 from here company and invests it for another 3 months to get

$A=(300+305.625)(1+\frac{0.075}{4})^{4\cdot \frac{1}{4}}=616.98$

again she gets 300 more so at 9 months she has

$A=(300+616.98)(1+\frac{0.075}{4})^{4\cdot \frac{1}{4}}=934.91$

one more time to get for the year

$A=(300+934.91)(1+\frac{0.075}{4})^{4\cdot \frac{1}{4}}=1257.31$

So it is better to take the 1300 at the end of the years :D