Question

Three thousand dollars is deposited at 8 percent interest compounded semiannually. What is the amount in the account at the end of 1 year? a. $3,588.00 b. $3,244.80 c. $4,876.90 d. $2,980.55 1000 ot earns 6 percent interest

Answer 1

the amount in the account at the end of 1 year will be;

`\text{ \$3,}244.80`

Step-by-step explanation:

Given that Three thousand dollars is deposited at 8 percent interest compounded semiannually.

`\begin{gathered} \text{ Principal P}=\text{ \$3,000} \\ \text{rate r = 8\% = 0.08} \\ \text{time t= 1 year} \\ \text{ number of times compounded n = 2 (semiannually)} \end{gathered}`

The future value F of a compound interest can be calculated using the formula;

`F=P(1+(r)/(n))^(nt)`

Substituting the given values into the formula;

`\begin{gathered} F=3,000(1+(0.08)/(2))^(2(1)) \\ F=3,000(1+0.04)^2 \\ F=3,000(1.04)^2 \\ F=3,000(1.0816) \\ F=3,244.80 \end{gathered}`

Therefore, the amount in the account at the end of 1 year will be;

`\text{ \$3,}244.80`