Question

Question 22

The future value, V, in dollars of an account with a monthly interest rate of i and
deposits on January 1st, February 1st and March 1st is given by the following equation
V = 50(1 + i)² + 100(1 + i) + 150. Which of the following equivalent expressions
contains the future value, as a constant or coefficient, for a monthly interest rate of
i = 0.1?
a. 50(i + 0.1)² + 190(i + 0.1) + 280.5
b. 50i² + 200i + 300
c.
50(i-0.1)² + 210(i - 0.1) + 320.5
d. 50(i + 2)² + 100

Answer 1

c. 50(i-0.1)² + 210(i - 0.1) + 320.5.

Explanation:

To find the equivalent expression that contains the future value for a monthly interest rate of i = 0.1, we simply substitute i = 0.1 into the equation V = 50(1 + i)² + 100(1 + i) + 150 and simplify.

V = 50(1 + 0.1)² + 100(1 + 0.1) + 150

V = 50(1.1)² + 100(1.1) + 150

V = 50(1.21) + 110 + 150

V = 60.5 + 110 + 150

V = 320.5

Therefore, the expression that contains the future value for a monthly interest rate of i = 0.1 is c. 50(i-0.1)² + 210(i - 0.1) + 320.5.