If $5,600 is deposited into an account paying 5% interest compounded annually (at the end of each year), how much money is in the account after 3 years?
This is what I get"
5600 X .05 =280 X 3 =840
But what happened to your original $5,600????
Also -- since the interest is compounded annually, at the end of the first year you'll have $5,600 + 280 = $5,880
At the end of the second year:
5,880 * 0.05 = 294
294 + 5,880 = $6,174
What will you have at the end of the third year?
I don't understand the reasoning behind your answer.
Anyway, the way to do this is the folliwing.
For every year your money is on the bank, the bank multiplies your balance by 1.05. This means that after 3 years, you get the following:
Money after 3 years = inititial deposit*1.05*1.05*1.05 = 5600 * 1.05^3 = 6482.7
you have calculated the simple interest earned by the account after 3 years.
So your account would have 5600 + 840 in it or $6440
in reality you would probably earn compound interest and the amount would be
5600(1.05)^3
= $6482.70
To calculate the amount of money in the account after 3 years with 5% interest compounded annually, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money in the account
P = the principal amount (initial deposit)
r = annual interest rate in decimal form
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $5,600
r = 5% = 0.05
n = 1 (compounded annually)
t = 3
Plugging these values into the formula:
A = 5600(1 + 0.05/1)^(1*3)
A = 5600(1 + 0.05)^3
A = 5600(1.05)^3
A ≈ 5600(1.157625)
A ≈ $6477.75
Therefore, there will be approximately $6,477.75 in the account after 3 years.