Homework Help: Precalc growth and decay

Posted by Kerrie on Sunday, April 19, 2009 at 5:20pm.

Alison deposits $500 into a new savings account that earns 5 percent interest compounded annually. If Alison makes no additional deposits or withdrawals, how many years will it take for the amount in the account to double?

the answer is 15 but i think its 14. please explain.

Precalc growth and decay - SraJMcGin, Sunday, April 19, 2009 at 7:13pm
I wonder also how the answer can be 15 years. Go to the following site, with the calculator for figuring out compound interest.

http://www.1728.com/compint.htm

Since you want to know how many years it will take:
1. click on YEARS
2. Input Principal = 500
3. Input Total = 1000
4. Input Rate = 5

I get: 14.2067!

Here's another calculator to use: http://www.moneychimp.com/calculator/compound_interest_calculator.htm

When I used 14 as the number of years = 989.97
When I used 15 as the number of years = 1039.46

You were only asked to end up with $1,000.00

Here's the formula : M = P(1+i)n

M = final amount including principal
P = principal amount
i = rate of interest per year
n - number of years invested

Most people use the compound interest calculator! Please check all your numbers carefully.

Sra
Precalc growth and decay - Reiny, Sunday, April 19, 2009 at 8:08pm
Sra is right.

The "calculator" on that webpage is using this formula
Amount = Principal(1+i)^n

we have 1000=500(1.05)^n
2 = 1.05^n
take log of both sides
log2 = log(1.05)^n
log2 = nlog1.05
n = log2/log1.05 = 14.2

after 14 years, your money has not yet doubled, close, but not yet.
Amount = 500(1.05)^14 = 989.97

So I guess they are right at 15, since you have to go into the 15th year to double your deposit.

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