Question 1

If the interest rate is 15% and will remain 15% forever, how much would a rational investor be willing to pay for an asset that will pay him 3,450 dollars 1 year from now, 1,322 dollars 2 years from now, and nothing at any other time?

Accepted Answer

The present value of the asset is calculated by discounting each cash flow at the interest rate of 15%. The present value of $3,450 received in 1 year is $3,450 / (1 + 0.15) = $3,000. The present value of $1,322 received in 2 years is $1,322 / (1 + 0.15)^2 = $1,000. Adding these gives $3,000 + $1,000 = $4,000.

Question 2

If the interest rate is 19% and will remain 19% forever, how much would a rational investor be willing to pay for an asset that will pay him 2,380 dollars 1 year from now, 1,416 dollars 2 years from now, and nothing at any other time?

Accepted Answer

The answer of If the interest rate is 19% and...

Question 3

The sum of the terms of the infinite geometric series 1, 0.83, 0.83², 0.83³, ...is closest to

Accepted Answer

The sum of an infinite geometric series with first term $ a $ and common ratio $ r $ (where $ |r| < 1 $) is given by $ \frac{a}{1-r} $. Here, $ a = 1 $ and $ r = 0.83 $, so the sum is $ \frac{1}{1-0.83} = \frac{1}{0.17} \approx 5.88 $.

Question 4

If the interest rate is 5% and will remain 5% forever, how much would a rational investor be willing to pay for an asset that will pay him 6,300 dollars 1 year from now, 1,102 dollars 2 years from now, and nothing at any other time?

Accepted Answer

The present value of the asset is calculated by discounting each cash flow at the interest rate of 5%. The present value of $6,300 received in 1 year is $6,300 / (1 + 0.05) = $6,000. The present value of $1,102 received in 2 years is $1,102 / (1 + 0.05)^2 = $1,000. The total present value is $6,000 + $1,000 = $7,000.

Question 5

The sum of the terms of the infinite geometric series 1, 0.78, 0.78², 0.78³, ...is closest to

Accepted Answer

The sum of an infinite geometric series is given by the formula S = a / (1 - r), where a is the first term and r is the common ratio. Here, a = 1 and r = 0.78. Thus, S = 1 / (1 - 0.78) = 1 / 0.22 = 4.5454... which is closest to 4.55.

Question 6

The sum of the terms of the infinite geometric series 1, 0.78, 0.78², 0.78³, ...is closest to

Accepted Answer

The sum of an infinite geometric series is given by the formula S = a / (1 - r), where a is the first term and r is the common ratio. Here, a = 1 and r = 0.78. Thus, S = 1 / (1 - 0.78) = 1 / 0.22 ≈ 4.55.

Question 7

The sum of the terms of the infinite geometric series 1, 0.95, 0.95², 0.95³, ...is closest to

Accepted Answer

The sum of an infinite geometric series is given by the formula S = a / (1 - r), where a is the first term and r is the common ratio. Here, a = 1 and r = 0.95. Thus, S = 1 / (1 - 0.95) = 1 / 0.05 = 20.

Question 8

If the interest rate is 13% and will remain 13% forever, how much would a rational investor be willing to pay for an asset that will pay him 6,780 dollars 1 year from now, 1,276 dollars 2 years from now, and nothing at any other time?

Accepted Answer

The answer of If the interest rate is 13% and...

Question 9

If the interest rate is 6% and will remain 6% forever, how much would a rational investor be willing to pay for an asset that will pay him 8,480 dollars 1 year from now, 1,123 dollars 2 years from now, and nothing at any other time?

Accepted Answer

To find the present value of the future cash flows, we discount each payment back to the present value using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods. For the $8,480 payment 1 year from now: PV = 8480 / (1 + 0.06)^1 = 8000. For the $1,123 payment 2 years from now: PV = 1123 / (1 + 0.06)^2 ≈ 1000. Adding these together gives $9,000.

Question 10

The sum of the terms of the infinite geometric series 1, 0.93, 0.93², 0.93³, ...is closest to

Accepted Answer

The sum of an infinite geometric series with first term 'a' and common ratio 'r' (where |r| < 1) is given by S = a / (1 - r). Here, a = 1 and r = 0.93, so S = 1 / (1 - 0.93) = 1 / 0.07 = 14.29.

Quiz 10: Asset Markets-Part B

If the interest rate is 15% and will remain 15% forever, how much would a rational investor be willing to pay for an asset that will pay him 3,450 dollars 1 year from now, 1,322 dollars 2 years from now, and nothing at any other time?

If the interest rate is 19% and will remain 19% forever, how much would a rational investor be willing to pay for an asset that will pay him 2,380 dollars 1 year from now, 1,416 dollars 2 years from now, and nothing at any other time?

The sum of the terms of the infinite geometric series 1, 0.83, 0.832, 0.833, ...is closest to

If the interest rate is 5% and will remain 5% forever, how much would a rational investor be willing to pay for an asset that will pay him 6,300 dollars 1 year from now, 1,102 dollars 2 years from now, and nothing at any other time?

The sum of the terms of the infinite geometric series 1, 0.78, 0.782, 0.783, ...is closest to

The sum of the terms of the infinite geometric series 1, 0.78, 0.782, 0.783, ...is closest to

The sum of the terms of the infinite geometric series 1, 0.95, 0.952, 0.953, ...is closest to

If the interest rate is 13% and will remain 13% forever, how much would a rational investor be willing to pay for an asset that will pay him 6,780 dollars 1 year from now, 1,276 dollars 2 years from now, and nothing at any other time?

If the interest rate is 6% and will remain 6% forever, how much would a rational investor be willing to pay for an asset that will pay him 8,480 dollars 1 year from now, 1,123 dollars 2 years from now, and nothing at any other time?

The sum of the terms of the infinite geometric series 1, 0.93, 0.932, 0.933, ...is closest to

The sum of the terms of the infinite geometric series 1, 0.83, 0.83², 0.83³, ...is closest to

The sum of the terms of the infinite geometric series 1, 0.78, 0.78², 0.78³, ...is closest to

The sum of the terms of the infinite geometric series 1, 0.78, 0.78², 0.78³, ...is closest to

The sum of the terms of the infinite geometric series 1, 0.95, 0.95², 0.95³, ...is closest to

The sum of the terms of the infinite geometric series 1, 0.93, 0.93², 0.93³, ...is closest to