Can someone help/check these problems please?! :)

[noname1234]

1. You hope to buy a house in 6 years. To save money for a down payment, suppose you being investing $250 per month in an annuity with a fixed rate of return at 7.6%. Assuming a continuous stream, how much will you have for your down payment at the end of 6 years?

This is how I set it up. Is this correct?
11
∑ $18000 (1 + 0.076/6) ^12-d
d=0

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2. The net profit of Wal-Mart Stores, Inc., the world's largest retailer, can be modeled as r(t) = 61.95t²-295.471t+525.843 million dollars per year t years after 1992. Assume that this net profit can be reinvested at 14% compounded continuously.

(a) How much would the net income invested since 1992 be worth in 2000?

(b) How much would this accumulated investment have been worth in 1992?

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3. The rate of change of U.S. consumption of beef from 1990 through 1995 can be modeled by b(t)= 199.26t-1.987 million pounds per year t years since 1990. Calculate the average rate of change of beef consumption between 1990 and 1995.

For that problem, I got 496.163 as my answer. Is this correct?

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4. Suppose that the demand for mailboxes can be modeled by D(p)=650(0.9)p thousand mailboxes where p is the price in dollars of the mailbox.

(a) Find the quantity of mailboxes consumers will purchase if the market price is $16

(b) Find the consumer's surplus when the market price is $16

 

[soroban]

Hello, noname1234!

1. You hope to buy a house in 6 years. To save money for a down payment,
suppose you being investing $250 per month in an annuity with a fixed rate of return at 7.6%.
How much will you have for your down payment at the end of 6 years?

This is how I set it up. \(\displaystyle \;\) Is this correct?

\(\displaystyle \L\;\;\sum^{11}_{d=0}\$18000(1\,+\,\frac{0.076}{6})^{12-d}\;\;\) . . . no

There are a number of errors:
\(\displaystyle \;\;\)You did not invest $18,000 at any time.
\(\displaystyle \;\;\)The montly interest rate is: \(\displaystyle \frac{0.076}{12}\)
\(\displaystyle \;\;\)What is that exponent? \(\displaystyle \;\)It should be the number of months.


This is an annuity which has the formula: \(\displaystyle \L\;A\;=\;D\,\frac{(1\,+\,i)^n\,-\,1}{i}\)

\(\displaystyle \;\;D\) = periodic deposit
\(\displaystyle \;\;\;i\) = periodic interest rate
\(\displaystyle \;\;\;n\) = number of periods
\(\displaystyle \;\;A\) = final amount

 

[noname1234]

I followed the formula in the book, maybe I used a wrong one? :shock: How do I solve for the other problems?

 

[noname1234]

Anyone?

 

[tkhunny]

I can torment you. How are you supposed to do such problems if You have no idea what formula or how to proceed? Do you have a book and a teacher? That would be a good place to start.