Question

In calculating the present value of $1,000 to be received 5 years from today, the discount factor has been calculated to be .7008. What is the apparent interest rate?

Answer 1

Answer:

7.37%

Explanation:

Assuming that the rate is compounded, the present value of an amount C to b e paid at the end of n years at an interest rate i is

$P.V=C*(1+\frac{i}{100} )^{-n}$

so the discounting factor for n years is;

$(1+\frac{i}{100})^{-n}$

In  our case;

$(1+\frac{i}{100})^{-5}=0.7008\\\\[(1+0.01i)^{-5}]^{-\frac{1}{5}}=0.7008^{-\frac{1}{5}}\\\\1+0.01i=0.7008^{-\frac{1}{5}}\\\\0.01i=0.7008^{-\frac{1}{5}}-1\\\\i=\frac{0.7008^{-\frac{1}{5}}-1}{0.01}\\ \\i=7.36956%$

Therefore, the apparent interest rate is 7.37% (rounded to 2 decimal places)