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Hello:

I have determined the solution to the following by using the proportion calculation that follows the question:

If $1000.00 earns $250.00 interest in 6 years, how much will earn $375 in 4 years?

$375/$250 = ?/$1000 (direct proportion)

6 yrs/4 yrs = ?/$1000 (indirect proportion)

Answer: $2250

My question is why are the 6 years indirectly proportional to the principal of $1000?

I can understand how the interest amount of $250.00 is directly proportional to $1000 because a larger principal will create a larger interest amount, but how is 6 years indirectly proportional to the principal of $1000?

I thank you for you reply and any helpful comments!

Let's examine this question a little more closely. Interest rates and earnings are a little more complicated than just proportions, but let's start off with the approach I think you're trying to use. Let the interest rate for one year be r, then

$1000･r･(6 years) = $250.

Solving for r gives r = 250/(1000･6).

If this same r is used for the 2nd calculation, then

new earnings = $375･r･4 years = 375･(250/(1000･6))･4 = $62.50

= (375/1000)･(4/6)･250

new earnings = ($375/$1000)･(4 years/6 years)･(previous earnings).

So the new earnings are directly proportional to the new principal ($375) and inversely proportional to the previous earnings ($1000). Likewise, the new earnings are directly proportional to the new duration (4 years) and inversely proportional to the old duration (6 years).

Your solution of $2250 is way too high. The lower value makes sense since the principal is smaller and the length of time is shorter.

Interest calculations over different periods (durations) actually take the form

earnings for 1 period = prinicipal･interest rate

Total earnings (original principal, P, plus interest earnings) for n periods = P(1+r)^n

which is more complicated than the calculation above.

Please let me know if this makes sense.

Randy

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