If the principal P = $500, the interest I = $100, and the rate r = 10%, find the following.

(a) What is the time?
years

(b) What is the future value?

100 = 500 * 0.1 * T

100 = 50T

2 = T

find the interest rate r at which $740 compounded annually growa to $800 in 2 years

To find the time (a) and future value (b) in this equation, we can use the following formulas:

(a) Time (t) = Interest (I) / (Principal (P) * Rate (r))
(b) Future value = Principal (P) + Interest (I)

Now, let's calculate each value.

(a) Time (t):
We are given:
Principal (P) = $500
Interest (I) = $100
Rate (r) = 10%

Using the formula, we have:
Time (t) = Interest (I) / (Principal (P) * Rate (r))
Time (t) = $100 / ($500 * 0.10)
Time (t) = $100 / $50
Time (t) = 2 years

Therefore, the time is 2 years.

(b) Future Value:
We are given:
Principal (P) = $500
Interest (I) = $100

Using the formula, we have:
Future value = Principal (P) + Interest (I)
Future value = $500 + $100
Future value = $600

Therefore, the future value is $600.