question: jevonte invested $37,000 in an account paying an interest rate of 1.7% compounded quarterly…

question: jevonte invested $37,000 in an account paying an interest rate of 1.7% compounded quarterly. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 14 years? show examples

question: jevonte invested $37,000 in an account paying an interest rate of 1.7% compounded quarterly. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 14 years? show examples

Answer

Explanation:

Step1: Identify 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. Here, $P=$37000$, $r = 0.017$, $n = 4$ (compounded quarterly), and $t = 14$.

Step2: Substitute values into the formula

$A=37000(1 +\frac{0.017}{4})^{4\times14}$ First, calculate the value inside the parentheses: $\frac{0.017}{4}=0.00425$, and $1+\frac{0.017}{4}=1.00425$. Then, calculate the exponent: $4\times14 = 56$. So, $A = 37000\times(1.00425)^{56}$.

Step3: Calculate $(1.00425)^{56}$

Using a calculator, $(1.00425)^{56}\approx1.26777$.

Step4: Calculate the final amount $A$

$A=37000\times1.26777 = 46907.49\approx46910$

Answer:

$46910$