Find the final amount of money in an account if $4,300 is deposited at 2% interest compounded semi-annually and the money is left for 10 years. What is the final amount rounded to the nearest cent?
4300 (1 + .01)^(2 * 10)
To calculate the final amount of money, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money
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 = $4,300
r = 2% = 0.02
n = 2 (compounded semi-annually)
t = 10 years
Plugging in the values into the formula, we get:
A = $4,300(1 + 0.02/2)^(2*10)
Simplifying further:
A = $4,300(1 + 0.01)^(20)
A = $4,300(1.01)^(20)
Calculating the expression in the parentheses:
(1.01)^20 ≈ 1.2214
A = $4,300 * 1.2214 ≈ $5,254.02
So, the final amount rounded to the nearest cent is approximately $5,254.02.
To find the final amount of money in the account, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
First, let's convert the annual interest rate to decimal form.
The annual interest rate is 2%, so we divide it by 100: r = 0.02
Since the interest is compounded semi-annually, n = 2 (twice a year).
Plugging in the values into the formula, we have:
A = $4,300 * (1 + 0.02/2)^(2*10)
A = $4,300 * (1 + 0.01)^(20)
A = $4,300 * (1.01)^(20)
Now, we can calculate the final amount by raising 1.01 to the power of 20 and multiplying it by the initial deposit of $4,300.
A = $4,300 * (1.01)^(20)
A ≈ $4,300 * 1.219
Rounding the final amount to the nearest cent gives us:
A ≈ $5,238.70
Therefore, the final amount in the account, rounded to the nearest cent, is $5,238.70.