Question

$100 is the principal deposited in a 5% saving account not compounded (simple interest). The same amount of $100 is placed in a 5% saving account compounded annually. Find the total amount A after t years in each saving plan and graph both of them in the same system of rectangular axes. Use the graphs to approximate the time it takes each saving plan to double the initial amount.

a) Simple interest plan doubles the initial amount faster.
b) Compound interest plan doubles the initial amount faster.
c) Both plans take the same amount of time to double the initial amount.
d) The information provided is insufficient to make a comparison.

Answer 1

To calculate the total future amount in simple and compound interest plans, use the formulas A = P + Prt and A = P(1 + r)^t respectively. Graph both plans using total amount A and number of years t. Calculate the time it takes to double the initial amount by finding the value of t when A = 2P.

Step-by-step explanation:

In a simple interest plan, the total future amount after t years can be calculated using the formula: A = P + Prt. In this case, P = $100, r = 0.05, and t is the number of years.

In a compound interest plan, the total future amount after t years can be calculated using the formula: A = P(1 + r)^t. In this case, P = $100, r = 0.05, and t is the number of years.

To graph both plans, we can plot the total amount A on the y-axis and the number of years t on the x-axis. We can then calculate the time it takes for each plan to double the initial amount by finding the value of t when A = 2P.