Suppose you just bought an annuity with 11 annual payments of $16,100 at the current interest rate of 12.75 percent per year. a.
What is the value of the investment at the current interest rate of 12.75 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What happens to the value of your investment if interest rates suddenly drop to 7.75 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What happens to the value of your investment if interest rates suddenly rise to 17.75 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
1 answer:
Answer and Explanation:
a. The value of the investment is shown below:
Given that,
Future value = $0
Rate of interest = 12.75%
NPER = 11 years
PMT = $16,100
The formula is shown below:
= -PV(Rate;NPER;PMT;FV;type)
So, after applying the above formula, the present value is $92,543.17
b. If the interest rate drop to 7.75%, so the present value is $116,344.48
c. If the interest rate rise to 17.75% so the present value is $75,670.82
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<h3>Explanation:</h3><h3>Part (a):</h3>
Solved part is attached as an image.
<h3>Part (b):</h3>Let us first determine the amount required of each item to produce 1 bracket.
From the attached diagram, we can see that to manufacture 1 bracket, quantity of each item needed is,
Base = 1
Spring = 2
Clamp = 1 + 4 = 5
Housing = 2
Handle = (1 * 1) + (4 * 1) = 5
Casting = (1 * 1) + (4 * 1) = 5
Bearing = 2 * 2 = 4
Shaft = 2 * 1 = 2
Hence, for 50 Brackets, quantity of each item required will be,
Base = 1 * 50 = 50
Spring = 2 * 50 = 100
Clamp = 5 * 50 = 250
Housing = 2 * 50 = 100
Handle = 5 * 50 = 250
Casting = 5 * 50 = 250
Bearing = 4 * 50 = 200
Shaft = 2 * 50 = 100
<em>NOTE: The above quantities give exclusive quantities required for each item. In actual practice, we won't have to purchase base, clamp & housing separately as the will be assembled from their components which are already procured.</em>
<h3>Part (c):</h3>As 25 bases are already in stock, parts for them will not be needed. I will refer the quantities subtracted due to this by indicating (B). Similarly, quantities subtracted due to clamps will be indicated as (C).
Base = 50 - 25 = 25
Spring = 50
Clamp = 250 - 100 - 25(B) = 125
Housing = 100 - (2*25)(B) = 50
Handle = 1 * 125 = 125
Casting = 1 * 125 = 125
Bearing = 2 * 50 = 100
Shaft = 1 * 50 = 50