# Precalc growth and decay

posted by on .

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?

• Precalc growth and decay - ,

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 - ,

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.