If the future value of $1 invested today at an interest rate of r% for n years is 9.6463, what is the present value of $1 to be received in n years at r% interest rate?
A) $9.6463
B) $1.00
C) $0.1037
D) None of the above

Question

Quizplus · Accepted Answer

The present value of $1 to be received in n years at r% interest rate can be found by using the formula:
present value = future value / (1 + r/100)^n
Here, we know the future value ($9.6463) and the interest rate (r%) and the number of years (n). Plugging those values into the formula, we get:
present value = 9.6463 / (1 + r/100)^n
Since we are looking for the present value when the future value is $1, we can plug in those values and solve for r:
1 = 9.6463 / (1 + r/100)^n
1 + r/100 = (9.6463)^(1/n)
r/100 = (9.6463)^(1/n) - 1
r = 100 * ((9.6463)^(1/n) - 1)
Substituting this value of r back into the original formula, we get:
present value = 1 / (1 + r/100)^n
Substituting the value of r, we get:
present value = 1 / (1 + 100 * ((9.6463)^(1/n) - 1)/100)^n
Simplifying this expression, we get:
present value = 1 / ((9.6463)^(1/n))^100
present value = 1 / 1.037
present value = 0.96463
Therefore, the present value of $1 to be received in n years at r% interest rate is $0.1037 (rounded to four decimal places).

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