[mathquestion]

Here is the question: Jan has $136.79 in her savings account. How long will she have to leave the money in the bank for her account to double, if the annual rate of interest is 9.75%?

Which calculation is correct? Any help would be great. Thanks!!

#1
my first attempt was to multiply $137.79 by 0.0975= 13.43
then divide 136.76 by 13.43= 10
so it would take 10 years to double the investment

but this seemed to easy to be right, so...


#2
in my second attempt I tried...
137.79x 0.0975= 13.43
13.43+ 137.79= 151.22(total of investment for 1st year)

151.22x 0.0975= 14.74
14.74+151.22= 165.96 (total investment for 2nd yr)

I calculated it this way until I got a total of $275.58 (double the amount of the investment)
My answer was seven years and five months. (264.26+ 10.73= $274.99)
I calculated $10.73 by dividing the 8th year of interest (25.76) by 12 (12 months in a year) and multiplying that number by 5.

[morgaine300]

First, you need to decide if it's 136.79 or 137.79. ;)

Unfortunately... depends on whether it's supposed to compound or not, because both answers could be correct.

I hate when problems don't say, but as a general rule, bank accounts like that are going to compound, which would make the second answer correct. But you did this by manually figuring out and adding interest on each year.

There's even an easier way to do it manually. Instead of multiplying by .0975 and then adding it to the prior principal, you can multiply by 1.0975 and you'll be right there. The 1 is the principal and it builds it into the answer. (i.e. it's 109.75%, which is the 100%, the principal, and the interest together. With the decimal moved over twice.)

So 137.79 x 1.0975 = 151.22

... and you're right to your answer without that extra step.

Then 151.22 x 1.0975... etc.

However, there's a shorter way by using this equation:



A is the maturity, P is the principal, i is interest per compounding period and n is total periods. (Since this is annual, the i is your .0975 and n will be years.)

To solve for the exponent, though, you need to know both algebra and use LN on your calculator. Have you been taught how to do that, or are supposed to be doing that? If not, just forget I said anything. If so, then someone can show you how to use this shorter method.

[ebaines]

A neat trick to use here is "the rule of 72." You divide the interest rate into 72, and the result is an approximation of how long it takes money to double - assuming compound interest. Here 72/9.75 = 7.38 years. It's not exact, but helpful for checking that your answer is in the ballpark.