marcus receives an inheritance of $14,000. he decides to invest this money in a 13 - year certificate of…

marcus receives an inheritance of $14,000. he decides to invest this money in a 13 - year certificate of deposit (cd) that pays 2.5% interest compounded monthly. how much money will marcus receive when he redeems the cd at the end of the 13 years? marcus will receive $ (round to the nearest cent.)

marcus receives an inheritance of $14,000. he decides to invest this money in a 13 - year certificate of deposit (cd) that pays 2.5% interest compounded monthly. how much money will marcus receive when he redeems the cd at the end of the 13 years? marcus will receive $ (round 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 $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert the given values to the appropriate form

We have $P=$14000$, $r = 2.5%=0.025$, $n = 12$ (compounded monthly), and $t = 13$ years.

Step3: Substitute the values into the formula

$A=14000(1 +\frac{0.025}{12})^{12\times13}$. First, calculate the value inside the parentheses: $\frac{0.025}{12}\approx0.0020833$, then $1+\frac{0.025}{12}=1 + 0.0020833=1.0020833$. Next, calculate the exponent: $12\times13 = 156$. So, $A = 14000\times(1.0020833)^{156}$. Using a calculator, $(1.0020833)^{156}\approx1.38977$. Then $A=14000\times1.38977=$19456.78$.

Answer:

$19456.78$