Question

Which of the following statements is FALSE?A. Across a longer time period, a single cash flow grows to a larger future valueB. For a higher interest rate, a single cash flow has a smaller present valueC. If its payments last longer, an annuity has a larger present valueD. For a higher interest rate, an annuity has a smaller future value

Answer 1

Answer:

D. For a higher interest rate, an annuity has a smaller future value

Explanation:

If the interest rate increases, then the capitalization factor on the annuity increases making the annuity future valeu increase:

$C \times \frac{(1+r)^{time} -1}{rate} = PV$

on the capitalziation factor we got rate in both part of the division:

$\frac{(1+r)^{time} -1}{rate}$

on the top part is being added a unit and power to t

while in the other it doesn't change.

While it is true that a higher dividend makes the quotient decrease, the increases in the top part exceeds by far the increase in the bottom part, making increase the quotient.