Question

A bank account has a beginning balance of $560.00. After 6 months, the balance in the account has increased to $572.60. What interest rate is being earned annually on this account?

Answer 1

The answer is 0.02

A = P(1 + r/n)ⁿˣ
A - the final amount
P - the principal (the initial amount)
r - the annual interest rate
n - the number of times that interest is compounded per year
x - the number of years

We have:
A = $572.60
P = $560.00
r = ?
n = 2
x = 1

572.60 = 560 * (1 + r/2)²*¹
572.60 = 560 * (1 + r/2)²
572.60 : 560 = (1 + r/2)²
572.60 = 1² + 2 * 1 * r/2 + (r/2)²
1.0225 = 1 + r + r²/4
4 * 1.0225 = 4 * 1 + 4 * r + 4 * r²/4
4.09 = 4 + 4r + r²
0 = 4 + 4r + r² - 4.09
0 = r² + 4r - 0.09
r² + 4r - 0.09 = 0


`r _(1,2) = \frac{-4+/- \sqrt{4^(2) -4*1*(-0.09)} }{2*1} = (-4+/- √(16+0.36) )/(2)= (-4+/- √(16.36) )/(2)= \\ \\ = (-4+/-4.04)/(2) \\ \\ r_1 = (-4-4.04)/(2) =-4.02 \\ \\ r_2 = (-4+4.04)/(2) =-0.02`

The rate cannot be negative, so it is 0.02