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.
You don't want the "rate of return" on each investment since it is already stated in each case, i.e., 6.5%, 7.8%, and 9.8%. What you want is the total worth of each investment at the end of its term:
a) $40,000 x 1.065^5=$54,803.47 Principal + interest compounded after 5 years.
b) $10,000 x 7.8% =$780 simple interest for 1 year
$780 x 5 =$3,900 simple interest for 5 years.
$10,000 + $3,900 =$13,900 principal + interest for 5 years.
c) This is a bit more complicated. First, you have to convert the interest rate from compounded semi-annually to compounded monthly to match the monthly deposits of $2,500 each.
9.8 /200 =0.049 + 1 =1.049^1/6 =1.00800475 - 1 =0.00800475 x 12 =9.61% compounded monthly.
Then you have to use this formula to find the FV of the deposits:
FV=P{[1 + R]^N - 1/ R}
FV =2,500[1 + 0.00800475]^(5*12) -1 / (0.00800475)}
FV=$191,588.49 - This is the balance in the acct. after 5 years.
As you can see, there is no comparison to c) investment. You may have made a mistake in the monthly payment of $2,500. It may be $250 per month. If that is the case, then you just divide the last answer of $191,588.49 by 10 =$19,158.85.
