You invested $1000 in a savings account in 6th grade. The account pays 5% annual interest. How much money will be in the account after 6 years? I understand how to set the equation up, but I'm not sure how to get the final answer. This is a question from my textbook that shows all the steps and the answer, but I can't figure out how they got a final answer of $1340.10. Please Help Me Understand This!!
They are using compound interest.
amount = 1000(1.05)^6
= 1340.0956..
= $ 1340.10
To calculate the final amount in the savings account after 6 years, you will need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or the loan is outstanding
Now let's plug in the values from your question:
P = $1000 (the initial investment)
r = 5% per year (as a decimal, so 0.05)
n = 1 (compounded annually)
t = 6 (number of years)
Using these values, the formula becomes:
A = 1000(1 + 0.05/1)^(1*6)
Simplifying the equation, we get:
A = 1000(1 + 0.05)^6
Calculating inside the parentheses first:
A = 1000(1.05)^6
Now, raise 1.05 to the power of 6:
A ≈ 1000(1.3401)
Finally, multiply the principal amount by the result:
A ≈ $1340.10
So, after 6 years, the amount in the savings account will be approximately $1340.10.
It's important to note that the textbook's answer may have been rounded to two decimal places, resulting in a slightly different final answer.