Question

What interest rate compounded quarterly is earned if an investment of $3000 grows to $5000 in 2 years?

Answer 1

We can use the compound interest formula:

$\small A = P(1+i)^n$

Where,
A = Amount
P = Principal amount invested
i = quarterly rate of interest
n = number of quarters. (2 years = 2*4 = 8 quarters)

Therefore,

$\small 5000 = 3000(1+i)^8$

$\small \frac{5000 }{3000}= (1+i)^8$

$\small (1+i)^8 = 1.66667$

$\small 1+i = \sqrt[8]{1.66667}$

$\small 1+i = 1.065936$

$\small i = 1.065936 - 1$

$\small = 0.065936$

OR

$\small =6.5936\%$

Since "i" is the quarterly interest rate, we have to multiply it with "4" to get annual interest rate.

Therefore,

Annual interest rate = 6.5936% * 4 = 26.37%