Sam Has $2000 that he plans to invest either in a CD or a savings account the value of the cd is given by the fraction A(t)=2,000(1.002)^t , were T is the time in years since the money was inves

Question

Sam Has $2000 that he plans to invest either in a CD or a savings account the value of the cd is given by the fraction A(t)=2,000(1.002)^t , were T is the time in years since the money was invested the value of the savings account over three months has given a table to the right which option will give him a higher return on his investment

time in months. Value in dollars

0. 2,000.00

1. 2,004.20

2. 2,008.41

3. 2012.62

find the monthly percent increase for the savings account.

find the equivalent monthly intrest rate for the cd

should Sam invest his money in the cd or savings account

Answer 1

A) To determine the monthly percent increase for the savings account:

1. Divide each value in the table by the one before it - this will give the growth factor for the table (savings account.
2. Subtract 1 from the growth factor obtained in order to get the interest rate in decimal form (since the values are increasing, we would have added 1 to the rate in order to get the growth factor)
3. Multiply that decimal by 100 to convert it back to percent

B) To find the equivalent monthly interest rate for the CD:

1. Since the function given contains the growth factor based on time in years, we need to convert it to months by recalling the interest function A(t) = P(1 + ^r/_n)^nt, where r is the rate in decimal form, n is the number of calculations and t is the time in years
2. In the case of the original function, n was assumed to be 1, for 1 year - the function was only used to calculate for each year that passed
3. Now, n is 12 for 12 months in a year. So, we have to get that rate in decimal form and divide it by 12 --> we want ^r/_n to be ^r/₁₂.
4. We do this by taking the growth factor they gave us, 1.002, and subtracting the 1 to get the rate by itself. We then divide that rate by 12. And that resulting answer would be the monthly interest rate. (Don't add 1 back to this! That will give you the new monthly growth factor. Also, multiplying by 100 will give you the new monthly percent increase and is unnecessary, as they only asked for monthly interest rate.)

C) To determine if Sam should invest his money in the CD or savings account:

1. Since both accounts are growing at an exponential rate, you can compare the monthly interest rates you calculated for both the CD and the savings account. When you do that, which monthly rate is greater? Which, then, would end up yielding the most money? Based on these answers, decide if Sam should invest his money in the CD or savings account, and be sure to explain why you made that decision! :-)