in 2010 staci invested $13,000 in a savings account for her new - born son. the account pays 3.8% interest…

in 2010 staci invested $13,000 in a savings account for her new - born son. the account pays 3.8% interest each year. determine the accrued value of the account in the year 2028, when her son will go to college. round your answer to the nearest cent. in the year 2028, the accrued value of the account will be $

in 2010 staci invested $13,000 in a savings account for her new - born son. the account pays 3.8% interest each year. determine the accrued value of the account in the year 2028, when her son will go to college. round your answer to the nearest cent. in the year 2028, the accrued value of the account will be $

Answer

Explanation:

Step1: Calculate the number of years

The initial year is 2010 and the final year is 2028. So the number of years $t=2028 - 2010=18$ years.

Step2: Use the compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Here, $P=$13000$, $r = 0.038$ (since $3.8%=0.038$), and $t = 18$. Substitute the values into the formula: $A=13000\times(1 + 0.038)^{18}$.

Step3: Calculate $(1 + 0.038)^{18}$

$(1 + 0.038)^{18}=1.038^{18}$. Using a calculator, $1.038^{18}\approx1.95797$.

Step4: Calculate the accrued value $A$

$A = 13000\times1.95797=$25453.61$.

Answer:

$25453.61$