Question

PLEASE HURRY
Jacquees deposited $1900 into an account that earns 4% interest compounded semiannually. After T years, Jacquees has $3875.79 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)= The value of investment after T years

- 2 years
-9 years
-18 years
-36 years

Answer 1

Answer:

t=18 years

Step-by-step explanation:

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

Answer 2

After 18 years he has $3875.79 in the account if Jacquees deposited $1900 into an account that earns 4% interest compounded semiannually option third is correct.

What is compound interest?

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

$\rm A = P(1+\dfrac{r}{n})^{nt}$

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

Jacquees deposited $1900 into an account that earns 4% interest compounded semiannually.

P = $1900

A = $3875.79

r = 4% = 0.04

n = 2

$\rm 3875.79 = 1900(1+\dfrac{0.04}{2})^{2t}$

After solving for t:

t = 18 years

Thus, after 18 years he has $3875.79 in the account if Jacquees deposited $1900 into an account that earns 4% interest compounded semiannually option third is correct.

Learn more about the compound interest here:

brainly.com/question/26457073

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