## Jacques deposited \$1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has \$3,875.79 in the a

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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2 months 2021-10-15T18:06:58+00:00 1 Answer 0 views 0

18 years

Step-by-step 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