Calculate the length of time for $400 to earn $160 if invested at 8% per annum, thank you in advance.
i dont know how to look into this question its ver hard
To calculate the length of time it takes for $400 to earn $160 at 8% per annum, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount accumulated
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, we have:
P = $400
A = $400 + $160 = $560
r = 8% = 0.08
n = 1 (since the interest is compounded annually)
Substituting the given values into the formula:
$560 = $400(1 + 0.08/1)^(1*t)
Divide both sides by $400 to isolate the exponential term:
1.4 = (1.08)^t
Take the logarithm of both sides:
log(1.4) = t * log(1.08)
Solve for t:
t = log(1.4) / log(1.08) ≈ 3.93
Therefore, it takes approximately 3.93 years for $400 to earn $160 at an interest rate of 8% per annum.
To calculate the length of time it takes for $400 to earn $160 at an interest rate of 8% per annum, you need to use the formula for simple interest:
Simple Interest (I) = Principal amount (P) * Rate of interest (R) * Time period (T)
Here, you want to find the time period (T), so rearrange the formula:
Time period (T) = Simple Interest (I) / (Principal amount (P) * Rate of interest (R))
In this case, the principal amount (P) is $400, the rate of interest (R) is 8% (or 0.08 as a decimal), and the simple interest (I) is $160.
Plug these values into the formula:
Time period (T) = $160 / ($400 * 0.08)
Time period (T) = $160 / $32
Time period (T) = 5 years
Therefore, it will take 5 years for $400 to earn $160 at an interest rate of 8% per annum.
You want t such that
compound interest: 400(1.08^t - 1) = 160
simple interest: 400*.08t = 160