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
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:
FB is the final balance in the account at the end.
P is the principal you started with, in this case $500.
i is the interest rate (use a small i so it doesn't get confused with a 1)
n is the number 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!!!