Vlad purchased some furniture for his apartment. The total cost was $ 2943.37. He paid $ 850 down and financed the rest for 18 months. At the end of the finance period .Vlad owed $ 2147.28 . What annual interest rate, compounded monthly , was he being charged ? Round your answer to two decimal places
To find the annual interest rate, compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount at the end of the finance period
P = Principal amount (initial amount financed)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, we know:
A = $2147.28 (amount owed at the end of the finance period)
P = $2943.37 - $850 = $2093.37 (principal amount financed)
n = 12 (compounded monthly)
t = 18/12 = 1.5 (18 months divided by 12 months in a year)
Now, let's substitute these values into the formula and find the annual interest rate (r):
$2147.28 = $2093.37(1 + r/12)^(12*1.5)
Dividing both sides by $2093.37:
$2147.28 / $2093.37 = (1 + r/12)^(18)
Taking the nth root of both sides (where n = 18):
((($2147.28 / $2093.37)^(1/18)) - 1) * 12 = r
Calculating this using a calculator, we find that r ≈ 0.072, or 7.2% (rounded to two decimal places).
Therefore, Vlad was being charged an annual interest rate of approximately 7.2%, compounded monthly.