Question

Consider a series of $110 end-of-period CFs spanning 2051-2056 and a $126 CF at the beginning of 2023. The interest rate is 2.1%. What is the equivalent value of these CFs at the end of 2042?

Answer #1

Present value of CF's spanning 2051-2056 at the end of 2051 =

We will solve it using the formula of present value of annuity i.e.

Present value = $110 × [{1-(1+0.21)^{-6}}/0.021] =
$614.08

Now, present value of CF's spanning 2051-2056 at the end of 2023 =

Present value (A) = $614.08/(1+0.021)^{8} = $520.02

Now,

future value of CF of 2023 at the end of 2042 (B) = $126 ×
(1+0.021)^{20} = $190.94

Equivalent value of CF = A + B = $520.02 + $190.94 = $710.96 or $711

I have given complete and detailed solution of your problem, in case of any query you can comment and

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