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Consider a cashflow of $1,382 at the beginning of 2069. What is the equivalent uniform amount...

Consider a cashflow of $1,382 at the beginning of 2069. What is the equivalent uniform amount for a series of end-of-year cash flows from 2052-2056? (i = 2.1%) Show work on paper, not excel.

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Answer #1

Ans)- Given Cashflow of $1382 at the beginning of 2069.

Interest rate(r) = 2.1% =0.021

Le ‘X’ be the required equivalent uniform amount for a-series of end of year cash flows 2052-2056.

So,

Cash flow at the beginning of 2069 = CF@2052 + (1+r)16 + CF@2053 + (1+r)15 + CF@2054 *(1+r) 14 + CF@2055*(1 + r)13 + CF@2056*

Cash flow at the beginning of 2069 = X(1 +0.021)16 + X(1 + 0.021)15 + X(1 + 0.021)14 + X(1 +0.021)13 + X(1 + 0.021)12

1382 = 1.3945X + 1.3658X + 1.3377X + 1.3102X + 1.2832X

1382 = 6.6914X

X 1382 6.6914 $206.53376

Hence the required equivalent Uniform amount for series of end-of-year cash flows from 2052-2056 is $206.53376.

Note: For $X invested at the end of period 2052,2053,2054,2055 and 2056 the compounding period will be 16,15,14,13 and 12 respectively to find the equivalent value at the beginning of 2069.

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