What simple interest rate is equivalent to a compound interest rate of 6% p.a. over 10 years correct to two decimal places?
wtf am i looking at not helpful man im 13
wtf
Oh, interest rates and decimals, my favorite! Let's see if we can find an answer that won't make your head spin faster than a clown on a unicycle.
Now, to figure out the simple interest rate equivalent to a compound interest rate of 6% over 10 years, let's break it down. Compound interest gets all fancy and starts to accumulate interest on top of interest. Simple interest is more straightforward and earns interest only on the original amount.
So, if we want an equivalent simple interest rate, we need to find the rate that will give us the same amount of interest after 10 years. Taking into account two decimal places, I suggest we look for a magnifying glass to get a closer look.
After carefully analyzing my clown-sized calculator, it seems that the equivalent simple interest rate would be 5.46% p.a. (rounding to two decimal places). Just remember, this is strictly for entertainment purposes! So, please consult with a financial expert if you require actual advice.
To find the equivalent simple interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = principal (initial amount)
r = interest rate
n = number of times interest is compounded per year
t = time in years
In this case, we are given that the compound interest rate is 6% per year (0.06) and it is compounded once per year (n = 1). We need to find the equivalent simple interest rate, so we want to solve for r.
Let's assume the initial amount is $1. We can substitute the values into the formula and solve for A:
A = 1(1 + 0.06/1)^(1*10)
A = 1(1.06)^10
A = 1.790847...
Now, let's calculate the simple interest rate:
Simple Interest = (A - P) / (P * t) * 100%
Simple Interest = (1.790847... - 1) / (1 * 10) * 100%
Simple Interest = 0.790847... / 10 * 100%
Simple Interest = 7.90847...%
Therefore, the simple interest rate equivalent to a compound interest rate of 6% per annum over 10 years is approximately 7.91% per annum.
Let's compare the value of $1 at the end of 10 years at both types of interest:
compound: Value = 1(1.06)^10
simple: let the rate be r
interest = 1(10)(r) = 10r
value = 1 + 10r
so 1 + 10r = 1.06^10
10r = 1.790847... - 1
r = .0790847...
rate = 7.91% to 2 decimals