Question

Which one of the statements below doesn't give the present value (PV) of an annuity-immediate with block payments: $7 for the first 9 years and $11 for the next 6 years, considering an interest rate of 3%?

a) $PV = \frac{7(1 - (1 + 0.03)^{-9})}{0.03} + \frac{11(1 - (1 + 0.03)^{-6})}{0.03}$
b) $PV = \frac{7(1 - (1 + 0.03)^{-9})}{0.03} + \frac{11(1 - (1 + 0.03)^{-3})}{0.03}$
c) $PV = \frac{7(1 - (1 + 0.03)^{-6})}{0.03} + \frac{11(1 - (1 + 0.03)^{-9})}{0.03}$
d) $PV = \frac{7(1 - (1 + 0.03)^{-3})}{0.03} + \frac{11(1 - (1 + 0.03)^{-6})}{0.03}$

Answer 1

Option b) $PV = \frac{7(1 - (1 + 0.03)^{-9})}{0.03} + \frac{11(1 - (1 + 0.03)^{-3})}{0.03}$ Option B is correct.

Step-by-step explanation:

The correct statement that doesn't give the present value (PV) of an annuity-immediate with block payments: $7 for the first 9 years and $11 for the next 6 years, considering an interest rate of 3% is option b) $PV = \frac{7(1 - (1 + 0.03)^{-9})}{0.03} + \frac{11(1 - (1 + 0.03)^{-3})}{0.03}$.

To find the present value of an annuity-immediate, we can use the formula PV = \frac{R(1 - (1 + r)^{-n})}{r}, where PV is the present value, R is the payment amount per period, r is the interest rate per period, and n is the number of periods.

In this case, we have R = $7 for the first 9 years, R = $11 for the next 6 years, r = 0.03 (3% as a decimal), and n = 9 for the first block of payments and n = 6 for the second block of payments.

Plug in the values into the given options and calculate the present value using the formula. Option b) gives the incorrect present value because it uses the wrong value for n in the second block of payments.