Question 1

Your mortgage requires that you pay $12,000 at the end of each of the next 30 years.If the annual interest rate is 12%,then you must have borrowed approximately:&#10;A) $117,660.&#10;B) $96,660.&#10;C) $78,660.&#10;D) $63,660.&#10;E) $133,660.

Accepted Answer

This is a case of annuity where a fixed payment is made at regular intervals. Using the formula for present value of an annuity, we get: PV = PMT x [1 - (1 + r)^-n] / r, where PV is the present value, PMT is the payment, r is the interest rate per period, and n is the number of periods. Plugging in the values, we get: PV = 12000 x [1 - (1 + 0.12)^-30] / 0.12 = $96,659.67. So, the closest option is B, $96,660.

Question 2

You borrow money from Fast Eddie's Fast Cash at 20% per year interest and agree to pay $500 at the end of each of the next four years.You must have borrowed approximately:&#10;A) $2,000.&#10;B) $1,595.&#10;C) $1,295.&#10;D) $1,095.&#10;E) $895.

Accepted Answer

The present value of an annuity formula is used to calculate the amount borrowed. The formula is PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($500), r is the interest rate (20% or 0.20), and n is the number of years (4). Plugging in the values, PV = $500 × [(1 - (1 + 0.20)^-4) / 0.20] ≈ $1,295.

Question 3

You've just won the $25 million lottery.You are going to receive a check for $1 million today and at the end of every year for the next 24 years.If the interest rate is 10%,the present value of your prize is:

A) $8,984,744.
B) $9,984,744.
C) $12,984,744.
D) $20,000,000.
E) $25,000,000.

A

Accepted Answer

To calculate the present value of the prize, we need to discount each of the 25 payments by the interest rate. Using the formula for the present value of an annuity, we get:

PV = (1 - (1 + r)^-n) x PMT / r
PV = (1 - (1 + 0.1)^-25) x 1,000,000 / 0.1
PV = $8,984,744

Therefore, the present value of the prize is $8,984,744, and the best choice is A.

Question 4

If the annual interest rate is i,the present value of a payment of $X to be received n years from now forever is: A) $X/(1 + i). B) $X/i. C) $X/(1 + i )ⁿ. D) $X/i ⁿ. E) none of the above.

Accepted Answer

The formula for present value of a perpetuity is PV = X / i, where X is the payment and i is the annual interest rate. However, since the payment is received n years from now, we need to discount it by (1 + i)^n. Therefore, the present value of the payment is X / (i * (1 + i)^n).

Question 5

If the annual interest rate is i,the present value of $X to be received at the end of each future year forever is: A) $X/(1 + i). B) $X/i. C) $X/(1 + i)ⁿ. D) $X/i ⁿ. E) $Xⁿ/i ⁿ.

Accepted Answer

The present value of $X to be received at the end of each future year forever, known as a perpetuity, is calculated as $X divided by the annual interest rate i, which is represented by the formula $X/i.

Question 6

If the annual interest rate is i,the present value of $X to be received at the end of each of the next n years is: A) $X/i. B) $X/(1 + i)ⁿ. C) D) $X[(1 + i)ⁿ] / [ i(1 + i)ⁿ - 1]. E) $X / [i(1 + i)ⁿ - 1].

Accepted Answer

The correct formula to find the present value of an annuity is $ \$ X \sum_{t=1}^{n} 1 /(1+i)^{t} $. This formula takes into account the time value of money by discounting each payment back to its present value using the interest rate i. Option A is incorrect because it only calculates the present value of one payment, not an annuity. Option B is a garbled mix of various finance formulas and does not accurately represent the present value of an annuity. Option D and E include unnecessary and incorrect calculations, making them incorrect choices.

Question 7

You buy your child a $100 savings bond that matures in 10 years and pays an annual interest rate of 10%.At maturity the bond will be worth:&#10;A) $228.17.&#10;B) $200.&#10;C) $259.37.&#10;D) $271.17.&#10;E) $217.71.

Accepted Answer

The value of the bond at maturity can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($100), r is the annual interest rate (10% or 0.10), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. Since the bond pays an annual interest rate and doesn't specify compounding more frequently, we assume n = 1. Therefore, A = $100(1 + 0.10)^10 = $100(1.10)^10 = $259.37.

Question 8

If the annual interest rate is 25%,the present discounted value of $100 to be received in one year is:&#10;A) $75.&#10;B) $80.&#10;C) $100.&#10;D) $120.&#10;E) $125.

Accepted Answer

The present discounted value formula is: present value = future value / (1 + interest rate)^n.
Plugging in the values, we get present value = 100 / (1 + 0.25)^1 = $80. Therefore, the best choice is B.

Question 9

The present value of expected future profits will if the discount rate increases and will if expected future profits increase.&#10;A) increase; not change&#10;B) increase; increase&#10;C) not change; decrease&#10;D) decrease; increase&#10;E) decrease; decrease

Accepted Answer

According to the formula for present value, as the discount rate (or required rate of return) increases, the present value decreases. Therefore, if the discount rate increases, the present value of expected future profits will decrease. On the other hand, if expected future profits increase, the present value will increase. Therefore, the correct answer is D, decrease; increase.

Deck 19: Appendix Problems