Question

Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has $3,875.79 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account?

2 years

9 years

18 years

36 years

Answer 1

3875.79=1900(1+0.04/2)^2t
Solve for t
t=(log(3,875.79÷1,900)÷log(1+0.04÷2))÷2
t=18 years

Answer 2

The correct option is C. 18 years

Explanation:

Principal = $1900

Rate of interest, r = 4%

The interest is compounded semi annually ⇒ n = 2

Amount = $3875.79

We need to find the time for which the money was in the account.

`Amount = Principal* (1+(rate)/(n* 100))^(n* time)\\\\\implies 3875.79=1900* (1+(4)/(100* 2))^(2* time)\\\\\implies (3875.79)/(1900)=(1.02)^(2* time)\\\\\implies 2.04 = (1.02)^(2* time)\\\\\implies 2* time = 36\\\\\implies time = 18`

Hence, The money was in the account for 18 years

Therefore, The correct option is C. 18 years