# I need help with this story problem:suppose one of your ansestors invested $500 in 1800 in an account paying 4% interst compound annually. Find the account balance in 2000 and 2100

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### 2 Answers

raely's answer tells you how to calculate **simple **interest. This problem calls for **compound** interest.

With **simple** interest, you figure out what the amount of interest is in the first year -- here it would be $500 x .04 = $20. You would get that same $20 added every year, so all you would have to do is figure out how many years' worth of $20s you are adding to the original principal amount.

Calculating **compound** interest is more difficult. In this case, each year you calculate the amount of interest for that year based on the principal + interest from the past. So, with this problem, in year 1 you get $20 interest. In year 2, the interest is reinvested and becomes part of the principal. So, year 2's interest is 4% of $520, or almost $21. The principal plus reinvested interest will keep growing every year, and so the amount of interest received each year will also continue growing.

Here's the formula for figuring it out:

FBis thefinalbalance in the account at the end.

Pis theprincipal you started with, in this case $500.

iis theinterest rate (use a small i so it doesn't get confused with a 1)

nis thenumber of years the money is invested.The formula: FB = P (1 + i)^n [^n means to the nth power]

So, plugging in what we know for this problem, the final balance in the year 2000 will be:

FB = 500 (1 + .04)^200

This isn't a very easy problem to calculate, because you have to figure out 1.04 x 1.04 x 1.04 . . . 200 times!!

There are compound interest calculators on the web that can do this for you! Here's a link to one. Be sure to read carefully what numbers you need to plug in where!!!

2000: 10,4000

2100: 15,600

Take the original amount times the interest, add the original amount and then multiply by the amount of years to get the total for that # of years.