math help needed

Question

A person invests $1,500 in an account that earns 5.5% interest compounded annually. let f(t) be the value (in dollars) of the account after t years.Give an equation for f

-f(t)=

-What will the value of the account be a be after 5 years ? Round your answer to the nearest cent. $__

-After 10 years? Round your answer to the nearest cent.

Answer 1

A) The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

Where: A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

Using this formula, we can write the equation for f(t) as:

f(t) = 1500(1 + 0.055/1)^(1*t) f(t) = 1500(1.055)^t

B) After 5 years, we can substitute t = 5 in the equation for f(t) to find the value of the account:

f(5) = 1500(1.055)^5 f(5) = 1500(1.307) = $1,960.50

So the value of the account after 5 years is $1,960.50 (rounded to the nearest cent).

C) Similarly, after 10 years we have:

f(10) = 1500(1.055)^10 f(10) = 1500(1.628) = $2,441.80

Thus, the value of the account after 10 years is $2,441.80 (rounded to the nearest cent).