190k views
3 votes
unfortunately, the set up of these problems is very confusing for me because they keep altering and changing per problem

unfortunately, the set up of these problems is very confusing for me because they-example-1
User Simpleuser
by
9.3k points

2 Answers

3 votes

Answer:

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.

User Matleg
by
8.0k points
4 votes

Answer:

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

User Akivajgordon
by
7.5k points

No related questions found