Question

Jennifer deposited $10,000 in the account that earns compound interest. The annual interest rate is 8%, and the interest is compounded two times a year. The current balance in the account is $10,400. how long has the money been invested?

Answer 1

V = P(1 + i)^n

Where,

V = 10.400
P = 10.000
i = 8%
n = ?


Then we will following:

10.400 = 10.000(1+8%)^n

10.400/10.000 = (1 +0,08)^n

1,04 = 1,08^n

Applying Logarithm on both sides, we will have:


Log (1,04) = Log(1,08^n)

Log(1,04) = n.Log(1,08)

n = Log(1,04)÷Log(1,08)

n = 0,5 years


Aplication rules of 3


1 years _______ 12months

0,5 years _______ x


x = 0,5 . 12 months

x = 6 months