Barry Newman's savings account has a balance of $2707. After 4 years, what will the amount of interest be at 5% compounded annually?
Well, Barry Newman seems to be a financially savvy fellow! Let's calculate that interest using some clown mathematics, shall we?
Okie-dokie! To calculate compound interest, we use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Barry's savings account balance is $2707. So, P = $2707.
The interest rate is 5% per year, which can be written as 0.05 in decimal form. So, r = 0.05.
Since the interest is compounded annually, n = 1.
Finally, we'll calculate for 4 years, so t = 4.
Now, let's plug those numbers into the formula and see what we get. *clownishly scribbles on a chalkboard*
A = 2707(1 + 0.05/1)^(1*4)
Calculating... *clownishly flips calculator multiple times*
Drumroll, please! The amount of interest at the end of 4 years, compounded annually at 5%, will be approximately...*clownishly taps fingers on desk* $321.60!
So, ta-da! Barry can expect approximately $321.60 of interest in his savings account after 4 years. Keep saving, Barry! *honks clown nose*
To find the amount of interest on Barry Newman's savings account after 4 years at 5% compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal balance (initial amount)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, the initial amount (P) is $2707, the annual interest rate (r) is 5% or 0.05 (expressed as a decimal), the number of times interest is compounded per year (n) is 1, and the number of years (t) is 4.
Substituting these values into the formula, we get:
A = 2707(1 + 0.05/1)^(1*4)
Simplifying further:
A = 2707(1.05)^4
Calculating:
A ≈ 2707 * 1.21550625
A ≈ $3297.73
Therefore, after 4 years, the amount of interest on Barry Newman's savings account at 5% compounded annually will be approximately $3297.73 - $2707 = $590.73.
To find the amount of interest on Barry Newman's savings account after 4 years at a 5% interest rate compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account (including both the principal and the interest)
P = the principal amount (initial balance of the savings account)
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $2707, the annual interest rate (r) is 5% or 0.05 (since it's expressed as a decimal), the compounding is annual (n = 1), and the time period (t) is 4 years.
Plugging the values into the formula, we get:
A = 2707(1 + 0.05/1)^(1*4)
Let's simplify this equation step by step:
A = 2707(1 + 0.05)^(4)
= 2707(1.05)^(4)
= 2707(1.21550625)
= 3295.48
Therefore, the future value of the account after 4 years will be $3295.48
To find the amount of interest, we subtract the principal amount (P) from the future value (A):
Interest = A - P
= 3295.48 - 2707
= 588.48
So, the amount of interest on Barry Newman's savings account after 4 years at a 5% interest rate compounded annually will be $588.48.
2707 * 1.05 = 2842.35 > end of year 1
2842.35 * 1.05 = 2984.4675 > end of year 2
Take it from there.