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Use the formula for the sum of a finite series and substitute P for the value of a, the monthly payment you just found. Also, substitute 1 + i for the r value in the formula since the rate of increase is now 1 + the interest rate = i. Now rewrite the formula with the substituted values in simplest form. That simplified formula will determine the future value of a structured savings plan with recurring deposits.

Respuesta :

Answer:

[tex]F.V.=\dfrac{P[(1+i)^n-1]}{i}[/tex]

Step-by-step explanation:

Sum of  finite geometric series, [tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

  • Substitute P for the value of a
  • Substitute 1 + i for r

That gives us:

[tex]F.V.=\dfrac{P[(1+i)^n-1]}{(1+i)-1}\\\\=\dfrac{P[(1+i)^n-1]}{1+i-1}\\\\F.V.=\dfrac{P[(1+i)^n-1]}{i}[/tex]

Where:

  • F.V.=Future Value
  • P=Recurring deposits.
  • i=Interest Rate
  • n=Number of deposits

This is the formula that is used to determine the future value of a structured savings plan with recurring deposits.

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