Thomas buys a new PLasma tv that costs 3500. He puts 300 down and borrows the rest. After 3 years he owes 3500. What annual interest rate, compounded semi-annually was Thomas being charged.
A=P(1 + i)^n
Sub in the numbers you know : )
i found the answer
To find the annual interest rate charged to Thomas, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = Total amount owed after t years
P = Principal amount (amount borrowed)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, we know:
Principal amount (P) = $3,200 (since Thomas put $300 down and borrowed the remaining $3,200)
Total amount owed (A) = $3,500
Number of times interest is compounded per year (n) = 2 (compounded semi-annually)
Number of years (t) = 3
We need to find the annual interest rate (r).
Rearranging the formula, we can solve for r:
r = ( (A/P)^(1/(n*t)) ) - 1
Calculating:
r = ( ($3,500/$3,200)^(1/(2*3)) ) - 1
r = (1.09375)^(1/6) - 1
r = 0.045 - 1
r ≈ 0.045
The annual interest rate, compounded semi-annually, that Thomas was being charged is approximately 0.045 or 4.5%.