If money is invested for 3 years , with interest compounded annually, the future value of the investment varies directly as the cube of ( $( 1 + r )$ r), where r is the annual interest rate. If the future value of the investment is $4499.46
When the interest rate is 4%, what rate gives a future value of $4244.83?
A) 4%
B) 2%
C) 0.02%
D) 20%

Question

Quizplus · Accepted Answer

The future value of an investment with compound interest is given by the formula $FV = P(1 + r)^n$, where $FV$ is the future value, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years. The problem states that the future value varies directly as the cube of $(1 + r)$, implying $FV \propto (1 + r)^3$. Given that the future value decreases when the interest rate changes from 4% to an unknown rate for the same investment period and principal, we can deduce that the new rate must be lower than 4%. Among the options, 2% is the only rate lower than 4% that would result in a decrease in future value, assuming all other factors remain constant.

If Money Is Invested for 3 Years , with Interest (1+r)( 1 + r )(1+r)

If Money Is Invested for 3 Years , with Interest $( 1 + r )$