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Korvikt [17]
3 years ago
8

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
Business
2 answers:
kupik [55]3 years ago
3 0
A year has two semesters, then
n = 2<span>v(t)=p<span><span>(<span>1+<span>r/2</span></span>)</span><span>2t
</span></span></span><span>
3875.79 = 1900∗<span><span>(<span>1+(<span>0.04/2)</span></span>)^</span><span>2t
</span></span></span><span>
2.0398895 = <span><span>(<span>1+<span>0.042</span></span>)^</span><span>2t
</span></span></span>Apply natural logarithm on both sides

<span>ln(2.0398895) = ln<span>[<span><span>(<span>1+<span>0.042</span></span>)^</span><span>2t</span></span>]

Then simplify,
</span></span><span>0.712896 = 2t∗ln(1.02)

</span><span>t = <span>0.712896 / (<span>2∗ln(1.02))
</span></span></span><span><span>
t=18 years

I hope my answer helped you. Have a nice day!</span></span>
yarga [219]3 years ago
3 0

Answer:

18 years

Explanation:

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