Respuesta :
The amount of money in Carson's account after 14 years would be $5231.6
What is compound interest?
"Compound interest is the interest which is calculated from the original principal plus accumulated interest."
The formula to calculate the compound interest:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
where,
A : Final amount
P : Initial amount (principal)
R : interest rate in percentage
r : interest rate (R/100)
n: number of times the interest is compounded
t : the overall tenure
For given question,
P = $3900, R = 2.1%, n = 12 (as compounded monthly), t = 14
for R = 2.1%,
[tex]r=\frac{2.1}{100} \\r=0.021[/tex]
Now, we need to find the value of A.
Using the formula of compound interest,
⇒ [tex]A=3900 \times (1+\frac{0.021}{12} )^{12\times 14}[/tex]
⇒ [tex]A=3900\times (1+0.00175)^{168}[/tex]
⇒ [tex]A=3900\times(1.00175)^{168}[/tex]
⇒ [tex]A=3900\times 1.3414[/tex]
⇒ [tex]A=5231.61[/tex]
⇒ [tex]A\approx \$ 5231.6[/tex]
Hence, there would be $5231.6 in the account after 14 years.
Learn more about compound interest here:
https://brainly.com/question/25857212
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