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# You invest 1, 300 in a 10-year bond that gives you 4 ? % interest on 1, 300 each year for 10 years. Construct a function that represents the amount of interest

A word problem for learning about functions and domain and range.

### 2 Answers by Expert Tutors

Dattaprabhakar G. | Expert Tutor for Stat and Math at all levelsExpert Tutor for Stat and Math at all le...
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Lauren:

A minor point.

You are asked to "construct a function that represents the amount of interest."

The answer by Tutor Lessa R. assumes that interest is reinvested. From the formula given in Lessa R.'s answer, the function that represents the amount of compound interest in t years, I(t, C)), say,(the C in the forumla indicates compounding)  is   I(t, C)) = B(t) - P = P{(1+r)t - 1].   You can compute I(t,C) from Lessa R.'s answer to be \$624.32

The domain of the above function is three dimensional, a "point" in the domain is (P, r, t), where P is a positive real number, r is a real number between 0 and 1 (being a rate) and t is a non-negative integer, t = 0, 1, 2, ......  The range of the function I(t,C) is a positive real number.

If, on the other hand, the interest is taken out each year, the problem becomes that of simple interest.  If r is the rate of interest, Pr is the annual interest earned on the investment of P in one year. So, in t years the amount of simple interest earned is simply t (Pr).

So the the function that represents the amount of simple interest can be called I(t, S) = t(P)(r)  (S for simple),

The domain and range of  I(t,S) are the same as those of I(t,C).

In your problem I(10,S) = 10(1300)(0.04) = 520.  (Notice the difference I(t,C) - I(t,S), effect of compounding!)

Dattaprabhakar (Dr. G.)
Irvine, CA
Leesa R. |
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For interest that is compound – which based on the wording I am assuming that in this problem that the bond is compounded annually.

So the following function where:

B = future value of bond
P = dollars invested
r= annual interest rate
t = time in years

B(t) = P(1+r)t