question: fabian invested $30,000 in an account paying an interest rate of 2.9% compounded daily. assuming…

question: fabian invested $30,000 in an account paying an interest rate of 2.9% compounded daily. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years? answer: attempt 1 out of 2

question: fabian invested $30,000 in an account paying an interest rate of 2.9% compounded daily. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years? answer: attempt 1 out of 2

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula when compounded $n$ times a year is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years. Here, $P=$30000$, $r = 0.029$ (since $2.9%=0.029$), $n = 365$ (compounded daily), and $t = 13$.

Step2: Substitute values into formula

$A=30000(1 +\frac{0.029}{365})^{365\times13}$. First, calculate the value inside the parentheses: $\frac{0.029}{365}\approx0.00007945217$, then $1+\frac{0.029}{365}=1 + 0.00007945217=1.00007945217$. Next, calculate the exponent: $365\times13 = 4745$. Then, $(1.00007945217)^{4745}\approx1.44077$. Finally, $A = 30000\times1.44077=$43223.10$.

Answer:

$43223.10$