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3 years ago

9

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?

1 answer:

Lisa [10]3 years ago

4 0

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

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3 years ago

A company issues $16200000, 5.8%, 20-year bonds to yield 6% on January 1, 2020. Interest is paid on June 30 and December 31. The

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Answer:

The amount of interest expense which will be recognized in 2020 is $949,681.45.

Explanation:

The following are given in the question:

Bond value = $16200000

Bond interest rate = 5.8%

Proceed from bond = $15825541

Yield rate = 6%

The amount of interest expense which will be recognized in 2020 can now be calculated as follows:

Interest expense for January 1, 2020 to June 30, 2020 = Proceed from bond * Yield rate * (6 / 12) = $15825541 * 6% * (6 / 12) = $474,766.23

Discount amortized during first 6 months = Interest expense for January 1, 2020 to June 30, 2020 - (Bond value * Bond interest rate * (6 / 12)) = $474,766.23 - ($16200000 * 5.8% * (6 / 12)) = $474,766.23 - 469,800 = $4,966.23

Interest expense for July 1, 2020 to December 31, 2020 = (Proceed from bond + Discount amortized during first 6 months) * Yield rate * (6 / 12) = ($15825541 + $4,966.23) * 6% * (6 / 12) = $474,915.22

Interest expense to be recognized in 2020 = Interest expense for January 1, 2020 to June 30, 2020 + Interest expense for July 1, 2020 to December 31, 2020 = $474,766.23 + $474,915.22 = $949,681.45

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