Suppose the interest rate is 4%. a. Having $200 today is equivalent to having what amount in one year? b. Having $200 in one year is equivalent to having what amount today? c. Which would you prefer, $200 today or $200 in one year? Does your answer depend on when you need the money? Why or why not?

(a) $200 today is equivalent to having $208 in one year with 4% interest rate.

(b) $192.31 today would be equivalent to $200 in one year with 4% interest rate.

(c) true

Explanation:

(a) since simple interest is given as:

I = p x r x t/100

Where p = the principal amount

r = interest rate

t = number of years

Now, from the question our principal is $200 since we are to calculate the interest on it, and our rate is 4% as obvious from the question and as well as our time is 1year. Substituting these to the interest formula we get:

I = 200 x 4 x 1/100

And that gives $8 as the interest, therefore in one year the amount we shall have will be: $200 + $8 = $208

(b) assuming we have 200 as the amount, we have now, we can get the principal we had last year at 4% interest with the following

A = p(1 + rt/100)

Now our amount is assumed to be $200 for 1year at 4% interest rate, therefore we have:

200 = p(1+4 x 1/100)

This gives

200 = p x 1.04

which gives

200/1.04 = p

p = $192.31(to the nearest cents)

(c) The statement is obviously true, because the amount we buy things today are more expensive than the amount we bought them in previous years, so having $200 today is preferable because the interest on it is just so small and would be a waste of resources.    

7

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70 years.

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