John Lee's savings account has a balance of $4494. After 3 years, what will the amount of interest be at 5% compounded semiannually?
I got $674.10
amount after 3 years at 5% pa compounded semiannually
= 4494(1.025)^6 = 5211.66
so interest = 5211.66-4494 = 717.66
Thanks:)
To calculate the interest on John Lee's savings account balance after 3 years, compounded semiannually at a 5% interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (including interest)
P is the principal balance (initial amount)
r is the interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal balance (P) is $4494, the interest rate (r) is 5% or 0.05 as a decimal, interest is compounded semiannually (n = 2), and the time period (t) is 3 years.
Plugging in these values into the formula:
A = 4494(1 + 0.05/2)^(2*3)
Now we can calculate the interest:
A = 4494(1 + 0.025)^(6)
A = 4494(1.025)^(6)
Using a calculator or equation solver, we find:
A ≈ 4494(1.025)^6 ≈ 4494(1.15927) ≈ 5200.44
Therefore, the interest on John Lee's savings account after 3 years, compounded semiannually at a 5% interest rate, is approximately $5200.44 - $4494 = $706.44.