Question

unfortunately, the set up of these problems is very confusing for me because they keep altering and changing per problem

Answer 1

P = $2366.91

(maybe try answering without a comma)

Explanation:

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = final amount

P = principal amount (initial deposit)

e = Euler's number (approximately 2.71828)

r = annual interest rate (as a decimal)

t = time (in years)

We are given:

r = 6.5% = 0.065 (annual interest rate)

t = 12 years

A = $5000 (final amount)

So we can rearrange the formula to solve for P:

P = A / e^(rt)

Substituting the values:

P = 5000 / e^(0.065*12)

P = $2366.91 (rounded to the nearest cent)

Therefore, you would need to deposit $2366.91 in an account with a 6.5% interest rate, compounded continuously, to have $5000 in your account 12 years later.

Answer 2

2292.03

Explanation:

Start with the formula for continuously compounded interest.

Then substitute all given values in the formula.

Finally, solve for the only variable remaining.

`A = Pe^(rt)`

A = future value = $5000

P = principal (deposited amount) = unknown

r = 6.5% = 0.065

t = time = 12 years

`5000 = Pe^(0.065 * 12)`

`5000 = Pe^(0.78)`

`5000 = P * 2.18147`

`P = (5000)/(2.18147)`

`P = 2292.03`

Answer: $2292.03