tom deposited $4000 into an account with 3.5% interest, compounded semiannually. assuming that no…

tom deposited $4000 into an account with 3.5% interest, compounded semiannually. assuming that no withdrawals are made, how much will he have in the account after 9 years? do not round any intermediate computations, and round your answer to the nearest cent.

tom deposited $4000 into an account with 3.5% interest, compounded semiannually. assuming that no withdrawals are made, how much will he have in the account after 9 years? do not round any intermediate computations, and round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (P) is the principal amount, (r) is the annual interest rate (in decimal form), (n) is the number of times interest is compounded per year, and (t) is the number of years. Given (P=$4000), (r = 3.5%=0.035), (n = 2) (since it's compounded semiannually), and (t = 9) years.

Step2: Substitute the values into the formula

Substitute the values into the formula: [ \begin{align*} A&=4000\left(1+\frac{0.035}{2}\right)^{2\times9}\ &=4000\left(1 + 0.0175\right)^{18} \end{align*} ] First, calculate (1+0.0175=1.0175). Then, find ((1.0175)^{18}). Using a calculator, ((1.0175)^{18}\approx1.371017).

Step3: Calculate the final amount

Multiply (4000) by (1.371017): (A = 4000\times1.371017=$5484.07)

Answer:

(5484.07)