If the future value of $1 invested today at an interest rate of r percent for n years is 9.6463, what is the present value of $1 to be received in n years at r percent interest rate?
A)$9.6463
B)$1.0000
C)$0.1037
D)$0.4132

Question

Quizplus · Accepted Answer

The future value formula is given by $FV = PV(1+r)^n$, where $FV$ is the future value, $PV$ is the present value, $r$ is the interest rate, and $n$ is the number of years.

In this case, we know that $FV=9.6463$, $PV=1$ (since we are asked to find the present value of $1 to be received in n years), and $n$ and $r$ are unknown.

We can rearrange the formula to solve for $PV$:
$PV = \frac{FV}{(1+r)^n}$

Substituting the given values, we get:
$1 = \frac{9.6463}{(1+r)^n}$

Solving for $1+r$, we get:
$1+r = (9.6463)^{\frac{1}{n}}$

We can then substitute this back into the formula for $PV$:
$PV = \frac{FV}{(1+r)^n} = \frac{1}{(9.6463)^{\frac{1}{n}}}$

Using a calculator or estimating, we get $PV \approx 0.1037$. Therefore, the answer is C.

If the Future Value of $1 Invested Today at an Interest