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Chapter 17: Problem 79

An amount \(F\) is accumulated by investing a single amount \(P\) for \(n\) compounding periods with interest rate of \(i\). Select the formula that relates \(P\) to \(F\). a) \(P=F(1+i)^{-n}\) c) \(P=F(1+n)^{-i}\) b) \(P 5 \mathrm{~F}(11 \mathrm{i})-\mathrm{n}\) d) \(P=F(1+n i)^{-1}\)

Short Answer

Expert verified
Answer: P = F(1+i)^{-n}

Step by step solution

01

Recall the compound interest formula

The compound interest formula, which relates the principal amount (P), accumulated amount (F), interest rate (i), and the number of compounding periods (n), is given by the following equation: \(F = P(1 + i)^n\)
02

Rearrange the formula to find P

We need to find a formula that represents the relationship between P and F. To do this, we can simply rearrange the compound interest formula and solve for P. Divide both sides of the equation by \((1 + i)^n\): \(P = \frac{F}{(1 + i)^n}\)
03

Select the correct formula

Comparing the rearranged formula with the given options: a) \(P=F(1+i)^{-n}\) c) \(P=F(1+n)^{-i}\) b) \(P 5 \mathrm{~F}(11 \mathrm{i})-\mathrm{n}\) d) \(P=F(1+n i)^{-1}\) We can see that the formula in option (a) matches the rearranged compound interest formula we derived. Therefore, the correct formula relating \(P\) to \(F\) is: \(P = F(1+i)^{-n}\)

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