Answer:
the simple interest rate that is equivalent to a compound interest rate of 6% p.a. over 10 years is approximately 0.0790847 or 7.91% to two decimal places.
Step-by-step explanation:
To find the simple interest rate that is equivalent to a compound interest rate of 6% p.a. over 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (principal + interest)
P is the principal (initial amount)
r is the interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, we have:
A = P(1 + 0.06/1)^(1*10)
Since we are looking for the simple interest rate, we need to find the value of r that will give us the same final amount. The formula for simple interest is:
A = P(1 + rt)
So, let's solve for r:
A = P(1 + rt)
P(1 + 0.06/1)^(1*10) = P(1 + r*10)
Simplifying the equation:
(1 + 0.06)^(10) = 1 + 10r
1.06^(10) = 1 + 10r
Now, let's solve for r:
r = (1.06^(10) - 1)/10
Using a calculator, we find that 1.06^(10) ≈ 1.790847. Plugging this into the equation:
r ≈ (1.790847 - 1)/10 ≈ 0.0790847
Therefore, the simple interest rate that is equivalent to a compound interest rate of 6% p.a. over 10 years is approximately 0.0790847 or 7.91% to two decimal places.
