Question

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.

Answer 1

`F.V.=(P[(1+i)^n-1])/(i)`

Explanation:

Sum of finite geometric series,
`S_n=(a(r^n-1))/(r-1)`

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

That gives us:

`F.V.=(P[(1+i)^n-1])/((1+i)-1)\\\\=(P[(1+i)^n-1])/(1+i-1)\\\\F.V.=(P[(1+i)^n-1])/(i)`

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.