4.6k views
0 votes
How much less would the account be worth after 30 years if compounded monthly instead of continuously?

A) $1200
B) $1300
C) $1400
D) $1500

User DDJ
by
7.8k points

1 Answer

4 votes

Final answer:

To determine the initial investment needed for an account to grow to $10,000 with compound interest, formulas for both annual and continuous compounding are utilized, with the key variables including the principal amount, interest rate, compounding frequency, and investment duration.

Step-by-step explanation:

To calculate how much money one must put into a bank account with a given interest rate to achieve a certain amount in the future, we use the formula for compound interest. Given a 10% interest rate compounded annually, we want to find out the present value that will become $10,000 in ten years.

The formula for compound interest is:

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

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

For continuous compounding, the formula is:

A = Pe^(rt)

Where:
e = the base of the natural logarithm
r = the annual interest rate (as a decimal)
t = the time in years

To answer the question, we would need the initial investment amount (P) for both monthly and continuous compounding scenarios to achieve $10,000 after 30 years, and then find the difference between the two results.

User Yuro
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories