In reference to the financial mathematics, which of the following statements are correct?
A. Sinking fund is an annuity created for accumulating money that can be used for paying off a financial obligation at some future pre-decided date.
B. The compound annual growth rate (CAGR) is calculated by dividing the cumulative return by the number of years.
C. The average annual growth rate (AAGR) is linear measure that does not account for the effects of compounding.
D. Sinking fund is created to deposit surplus money which can be used for any future need.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A and C only
A sinking fund is built by regular deposits to meet a known liability on a fixed future date. The CAGR is the constant yearly rate that takes the beginning value to the ending value with compounding:
\( \displaystyle \text{CAGR}=\left(\frac{\text{Ending value}}{\text{Beginning value}}\right)^{1/n}-1 \)
The AAGR is the arithmetic mean of the yearly growth rates.
So a sinking fund is for a specific future obligation, CAGR uses an n-th root (compounding), and AAGR is a simple average (no compounding).
Checking the statements
(A) Sinking fund is an annuity created for accumulating money that can be used for paying off a financial obligation at some future pre-decided date. — Correct. This is the definition of a sinking fund.
(B) The compound annual growth rate (CAGR) is calculated by dividing the cumulative return by the number of years. — Incorrect. Dividing by the number of years gives a simple average; CAGR takes the n-th root of the growth ratio.
(C) The average annual growth rate (AAGR) is linear measure that does not account for the effects of compounding. — Correct. AAGR is the arithmetic mean of the yearly rates, so it ignores compounding.
(D) Sinking fund is created to deposit surplus money which can be used for any future need. — Incorrect. A sinking fund is set aside for a specific obligation, such as redeeming debentures or replacing a machine, not for any need.