Question

1. What is the present value on January 1, 2019, of $30,000 due on January 1, 2023, and discounted at 10% compounded annually? $ 20,490.40 X 2. What is the present value on January 1, 2019, of $40,000 due on January 1, 2023, and discounted at 11% compounded semiannually? $ 26,063.59 X 3. What is the present value on January 1, 2019, of $50,000 due on January 1, 2023, and discounted at 16% compounded quarterly? $ 26,695.41 x

I cannot figure out why these are wrong. Would appreciate help.

Answer 1

Answer (1)

Future value = $30,000

Time period (n) = 4 years

Discount rate (r) = 10%

Present value = Future value x Present value factor (r%, n)

= 30,000 x Present value factor (10%, 4)

= 30,000 x 0.68301

= $20,490.3

= $20,490 (Rounded to nearest whole dollar)

Present value on January 1, 2019, of $30,000 due on January 1, 2023, and discounted at 10% compounded annually = $20,490

Answer (2)

Future value on January 1, 2023 = $40,000

Discount rate = 11% compounded semiannually

Hence, discount rate (r) = 5.5%

Time period = 4 years

Time period (n) = 4 x 2

= 8 half year

Present value = Future value x Present value factor (r%, n)

= 40,000 x PVF (5.5%, 8)

= 40,000 x 0.65160

= $26,064

Hence, Present value on January 1, 2019 of $40,000 due on January 1, 2023 = $26,064

Answer (3)

Future value on January 1, 2023 = $50,000

Discount rate = 16% compounded quarterly

Hence, discount rate (r) = 16/4 = 4%

Time period = 4 years

Time period (n) = 4 x 4

= 16 quarter means 4 years

Present value = Future value x Present value factor (r%, n)

= 50,000 x PVF (4%, 4)

= 50,000 x 0.5339= $26,695.41

Hence, Present value on January 1, 2019 of $50,000 due on January 1, 2023 = $26,695.41