Asked by Shailee Woods on May 09, 2024
Verified
Clarence has been investing $1,000 at the end of every year at 11% compounded annually. With today's contribution his investment has grown to $44,500. How many years ago did he make the first contribution?
A) 26 years
B) 49 years
C) 17 years
D) 31 years
E) 12 years
Compounded Annually
Refers to the process where the interest on an investment or loan is calculated annually and added to the principal, so that the balance doesn't merely grow by the initial rate of interest but by the interest on the interest as well.
Contributions
Contributions are amounts of money or resources given by individuals or entities to a common fund or cause, often for charity, investments, or pooling resources.
Investment
Allocation of resources, usually money, in expectation of a future financial return or benefit.
- Appraise the time required to secure a financial milestone through consistent financial engagements or liquidations.
- Understand the concept of time value of money and its applications in financial calculations.
Verified Answer
ED
Explore Daily lifeMay 13, 2024
Final Answer :
C
Explanation :
The formula for the future value of a series of annuities (regular payments or contributions) is given by FV=P×(1+r)n−1rFV = P \times \frac{(1 + r)^n - 1}{r}FV=P×r(1+r)n−1 , where FVFVFV is the future value of the annuity, PPP is the payment amount, rrr is the annual interest rate, and nnn is the number of payments. Rearranging the formula to solve for nnn , we get n=log(FV×rP+1)log(1+r)n = \frac{\log(\frac{FV \times r}{P} + 1)}{\log(1 + r)}n=log(1+r)log(PFV×r+1) . Substituting FV=44500FV = 44500FV=44500 , P=1000P = 1000P=1000 , and r=0.11r = 0.11r=0.11 , we can solve for nnn . The calculation gives a value close to 17, indicating that Clarence made his first contribution 17 years ago.
Learning Objectives
- Appraise the time required to secure a financial milestone through consistent financial engagements or liquidations.
- Understand the concept of time value of money and its applications in financial calculations.