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?
Compound interest formula: V(t)= P 1-
t = years since initial deposit
n = number of times compounded per year
r= annual interest rate (as a decimal)
P = initial (principal) investment
VO) = value of investment after t years
2 years
9 years
18 years
36 years
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Answer 1

18 years

Explanation:

Formula: V(t) = P* (1 + r/2)^(2t)

r = 4% = 0.04

P =$1,900

V(t) = $1,900 *(1 + 0.04/2)^ (2t)

V = 1900 *(1.02)^(2t)

$3,875.79 = 1900 * 1.02^2t

3875.79/1900 = 1.02^ (2t)

2.0398894736842 = 1.02 ^(2t)

ln 2.0398894736842 = ln (1.02^(2t) )

ln 2.0398894736842 = 2*t*ln (1.02)

ln 2.0398894736842 /(2* ln (1.02)) = t

0.71289562682179 / (2 * 0.0198 ) = t

18.00002 years = t