compound discount is defined as:\n a) the accumulated amount\n b) the difference between f and p\n c) the…

compound discount is defined as:\n a) the accumulated amount\n b) the difference between f and p\n c) the effective rate\n d) the simple discount\n\nif p = 20,000 and grows to f = 25,000 in 3 years, compounded annually, the rate is closest to:\n a) 6.2%\n b) 8%\n c) 10%\n d) 12%

compound discount is defined as:\n a) the accumulated amount\n b) the difference between f and p\n c) the effective rate\n d) the simple discount\n\nif p = 20,000 and grows to f = 25,000 in 3 years, compounded annually, the rate is closest to:\n a) 6.2%\n b) 8%\n c) 10%\n d) 12%

Answer

Explanation:

Step1: Define compound discount

Compound discount is the difference between the future - value ($F$) and the present - value ($P$).

Step2: Solve for the interest rate in the compound - interest formula

The compound - interest formula is $F = P(1 + r)^n$, where $F$ is the future value, $P$ is the present value, $r$ is the annual interest rate, and $n$ is the number of years. Given $P = 20000$, $F = 25000$, and $n = 3$. We substitute these values into the formula: $25000=20000(1 + r)^3$. First, divide both sides by 20000: $\frac{25000}{20000}=(1 + r)^3$, so $1.25=(1 + r)^3$. Then take the cube - root of both sides: $1 + r=\sqrt[3]{1.25}$. $\sqrt[3]{1.25}\approx1.077$. So $r\approx1.077−1 = 0.077\approx8%$.

Answer:

  1. b) The difference between F and P
  2. b) 8%