104k views
5 votes
What is the accumulated value of ​$100 invested for 20 years at 6.3​% p.a. compounded

​(a)​ annually?
​(b)​ semi-annually? ​
(c)​ quarterly? ​
(d)​ monthly?

User Kumar D
by
8.3k points

1 Answer

1 vote

Final answer:

The accumulated value of $100 invested at 6.3% interest, compounded annually for 20 years, can be calculated using the compound interest formula for various compounding periods: annually, semi-annually, quarterly, and monthly. While the principal and rate remain consistent, the different compounding frequencies yield different amounts due to more frequent application of interest.

Step-by-step explanation:

The accumulated value of $100 invested at 6.3% per annum for 20 years can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where:

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

For part (a), compounded annually (n=1):

  • A = $100(1 + 0.063/1)^(1*20) = $100(1.063)^20

For part (b), compounded semi-annually (n=2):

  • A = $100(1 + 0.063/2)^(2*20) = $100(1.0315)^40

For part (c), compounded quarterly (n=4):

  • A = $100(1 + 0.063/4)^(4*20) = $100(1.01575)^80

For part (d), compounded monthly (n=12):

  • A = $100(1 + 0.063/12)^(12*20) = $100(1.00525)^240

Note: You would need to use a calculator to find the numerical value for each compound scenario.

User Grantley
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.