if $192 increased to $363 in 2 years. what is the interest rate
To calculate the interest rate, we can use the formula for simple interest:
{\displaystyle I=P\cdot r\cdot t}
where:
I = interest earned
P = principal amount (initial amount)
r = interest rate (unknown)
t = time in years
In this case, we know that the principal amount is $192 and it increased to $363 in 2 years. Therefore, the interest earned is:
{\displaystyle I=363-192=171}
Plugging in the values into the formula, we can rearrange it to solve for r:
{\displaystyle r={\frac {I} {P\cdot t}}}
Substituting the known values:
{\displaystyle r={\frac {171} {192\cdot 2}}}
Simplifying the equation:
{\displaystyle r={\frac {171} {384}}}
The interest rate is approximately 0.4453, or 44.53%.
If it's simple interest, then
192(1+2r) = 363
1+2r = 1.89
2r = .89
r = 44.5%
If it's anually compound interest then
192(1+r)^2 = 363
(1+r)^2 = 1.89
1+r = 1.374
r = 37.4%
Of course, interest compounded quarterly, monthly, daily, or continuously will have successively smaller interest rates.