kala deposited $4000 into an account with 2.1% interest, compounded monthly. assuming that no withdrawals…

kala deposited $4000 into an account with 2.1% interest, compounded monthly. assuming that no withdrawals are made, how much will she have in the account after 8 years? do not round any intermediate computations, and round your answer to the nearest cent.

kala deposited $4000 into an account with 2.1% interest, compounded monthly. assuming that no withdrawals are made, how much will she have in the account after 8 years? do not round any intermediate computations, and round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify compound interest formula

The formula for compound interest is $A = P\left(1+\frac{r}{n}\right)^{nt}$, where:

  • $A$ = final amount
  • $P$ = principal amount
  • $r$ = annual interest rate (decimal)
  • $n$ = number of times compounded per year
  • $t$ = time in years

Step2: Assign values to variables

$P = 4000$, $r = \frac{2.1}{100}=0.021$, $n=12$, $t=8$

Step3: Calculate periodic rate and total periods

$\frac{r}{n} = \frac{0.021}{12}=0.00175$ $nt = 12\times8=96$

Step4: Compute growth factor

$\left(1+0.00175\right)^{96} \approx 1.183197$

Step5: Calculate final amount

$A = 4000\times1.183197$

Answer:

$$4732.79$