Question

What is the present value on January 1, 2019, of $30,000 due on January 1, 2023, and discounted at 10% compounded annually? $ 95,095.96 What is the present value on January 1, 2019, of $40,000 due on January 1, 2023, and discounted at 11% compounded semiannually?

Answer 1

Answer:

$20,490.3

$26349.24

Explanation:

Data provided in the question:

Future value of the amount due on January 1, 2023 =  $30,000

Discount rate, r = 10% = 0.10

Time, n = 4 years          [from 2019 to 2023]

Now,

Future value = Present value × (1 + r)ⁿ

thus,

$30,000 = Present value × (1 + 0.1)⁴

or

$30,000 = Present value × 1.4641

or

Present value = $20,490.3

Case 2:

Future value of the amount due on January 1, 2023 =  $40,000

Discount rate, r = 11% = 0.11

Time, n = 4 years          [from 2019 to 2023]

Now,

Future value = Present value × (1 + r)ⁿ

thus,

$40,000 = Present value × (1 + 0.11)⁴

or

$40,000 = Present value × 1.51807041

or

Present value = $26349.24