Respuesta :
Answer:
$7499.82
Step-by-step explanation:
We have been given that a person places $6340 in an investment account earning an annual rate of 8.4%, compounded continuously. We are asked to find amount of money in the account after 2 years.
We will use continuous compounding formula to solve our given problem as:
[tex]A=Pe^{rt}[/tex], where
A = Final amount after t years,
P = Principal initially invested,
e = base of a natural logarithm,
r = Rate of interest in decimal form.
[tex]8.4\%=\frac{8.4}{100}=\frac{8.4}{100}=0.084[/tex]
Upon substituting our given values in above formula, we will get:
[tex]A=\$6340\cdot e^{0.084\cdot 2}[/tex]
[tex]A=\$6340\cdot e^{0.168}[/tex]
[tex]A=\$6340\cdot 1.1829366106478107[/tex]
[tex]A=\$7499.818111507119838[/tex]
Upon rounding to nearest cent, we will get:
[tex]A\approx \$7499.82[/tex]
Therefore, an amount of $7499.82 will be in account after 2 years.
Answer:
555.97
Step-by-step explanation:
A person places $207 in an investment account earning an annual rate of 5.2%, compounded continuously. Using the formula V = Pe^{rt}V=Pe
rt
, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 19 years.
r=5.2\%=0.052
r=5.2%=0.052
Move decimal over two places
P=207
P=207
Given as the pricipal
t=19
t=19
Given as the time
V=Pe^{rt}
V=Pe
rt
V=207e^{0.052( 19)}
V=207e
0.052(19)
Plug in
V=207e^{0.988}
V=207e
0.988
Multiply
V=555.9725\approx 555.97
V=555.9725≈555.97
Use calculator and round to nearest cent
Your Solution:
555.97
