Compound Interest and Futur Value

[charlesgipson]

The question is "You deposit $4500 per year at the end of each of the next 25 years into an account that pays 10% compounded annually. How much could you withdraw at the end of each of the 20 years following your last deposit if all withdrawals are the same dollar amount? (The twenty-fifth and last deposit is made at the beginning of the 20-year period. The first withdrawal is made at the end of the first year in the 20-year period.)

I know the formula for future value of an original deposit is FVn = PV(1+i)n which would be 48756 but what is the formula for having multiple deposits? This question seems to involve lots of formula's. It's like a multi-part question. Can you help? Thanks

 

[TchrWill]

The question is "You deposit $4500 per year at the end of each of the next 25 years into an account that pays 10% compounded annually. How much could you withdraw at the end of each of the 20 years following your last deposit if all withdrawals are the same dollar amount? (The twenty-fifth and last deposit is made at the beginning of the 20-year period. The first withdrawal is made at the end of the first year in the 20-year period.)

Assuming that the interest rate of 10%, compounded annualy, applies during the payout period also:


What will an amount of R dollars deposited in a savings bank at the end of each year for N years, and earning I% compounded annually, amount to in N years.

S = R[(1+i)^n - 1]/i.

S = 4500[(1.1)^25]/.1 = $442,562.

What is the amount that must be paid (Present Value) for an annuity with a periodic payment of R dollars to be made at the end of each year for N years, at an interest rate of I% compounded annually?

P = R[1 - (1 += i)^(-n)]/i

442,562 = R(1 - 1.1^(-20)]/.1 yielding R = $51,983.