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
Mark this and retum
Save and Exit
Nexs

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

Answers ( )

    0
    2021-10-15T18:08:09+00:00

    Answer:

    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

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )