If $3,000.00 is deposited into an account paying 3% interest compounded annually (at the end of each year), how much money is in the account after 4 years? (Round to the nearest cent.)
The compound interest formula is
Amount = P(1+r)n
where
P=principal,
r=rate of interest per period (year in this case). 5% per annum is written as 0.05
n=number of periods money is deposited.
For example,
$3000 deposited at 5% per annum for 2 years will yield, when compounded yearly:
Amount=3000*(1+0.05)2
=$3307.50
For 3000 invested at 3% interest compounded yearly for 4 years will yield an amount less than $3400 and in which the amount after the decimal point is $33--.53.
Principal is $5,000, rate if interest is 6.5%, and time to repayment is 3 years. Compute the compound interest
To determine how much money is in the account after 4 years with compound interest, we can use the formula:
A = P(1 + r/n)^(n*t)
Where:
A = the amount of money in the account after t years
P = the principal amount (initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $3,000.00, the annual interest rate (r) is 3% (or 0.03 as a decimal), interest is compounded annually (n = 1), and we want to find the amount of money after 4 years (t = 4).
Using the formula:
A = $3,000.00(1 + 0.03/1)^(1*4)
First, let's simplify the expression inside the parentheses:
A = $3,000.00(1 + 0.03)^(4)
Next, calculate the term inside the parentheses:
A = $3,000.00(1.03)^(4)
Now, raise 1.03 to the power of 4:
A = $3,000.00(1.12550875)
Finally, multiply the principal amount by the result:
A = $3,376.53
Therefore, there will be approximately $3,376.53 in the account after 4 years.