Question

Your client wants to accumulate $1,800,000 over the next 20 years by investing the same amount at the beginning of each month. If she can expect a long-term rate of return of 8.8% compounded annually, how much must she invest each month? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  The client must invest $ at the beginning of each month.

Please I need the each steps that how did you get the answer

Answer 1

Desired Sum = $1,800,000
Time Period = 20 years or 240 months
Annual Interest Rate = 8.80%

Monthly Interest Rate = (1 + Annual Interest Rate)^(1/12) - 1
Monthly Interest Rate = (1 + 0.0880)^(1/12) - 1
Monthly Interest Rate = 1.0070532 - 1
Monthly Interest Rate = 0.0070532 or 0.70532%

Let monthly saving at the beginning of each month is $x

$x*1.0070532^240 + $x*1.0070532^239 + … + $x*1.0070532^2 + $x*1.0070532 = $1,800,000
$x * 1.0070532 * (1.0070532^240 - 1) / 0.0070532 = $1,800,000
$x * 628.559805 = $1,800,000
$x = $2,863.69

Monthly saving = $2,863.69

The client must invest $2,863.69 at the beginning of each month.