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+r/n)^nt

t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years

Answer 1

A year has two semesters, then
n = 2v(t)=p(1+r/2)2t

3875.79 = 1900∗(1+(0.04/2))^2t

2.0398895 = (1+0.042)^2t
Apply natural logarithm on both sides

ln(2.0398895) = ln[(1+0.042)^2t]

Then simplify,
0.712896 = 2t∗ln(1.02)

t = 0.712896 / (2∗ln(1.02))

t=18 years

I hope my answer helped you. Have a nice day!

Answer 2

Answer:

18 years

Explanation: