Question

A young executive deposits $100 at the end of each month for 5 years into an account that earns 6% compounded monthly. How much is in the account after the 5 years? (Round your answer to the nearest cent).

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The executive then changes the deposits in order to have a total of $400,000 after 25 total years. What should be the revised monthly payment in order to meet the $400,000 goal? (Round your answer to the nearest cent).

$  

How much interest is earned during the 25 years?

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Answer 1

Answer a.

Monthly Deposit = $100
Time Period = 5 years or 60 months

Annual Interest Rate = 6.00%
Monthly Interest Rate = 6.00% / 12
Monthly Interest Rate = 0.50%

Accumulated Sum = $100*1.005^59 + $100*1.005^58 + ... + $100*1.005 + $100
Accumulated Sum = $100 * (1.005^60 - 1) / 0.005
Accumulated Sum = $100 * 69.7700
Accumulated Sum = $6,977.00

Answer b.

Current Balance = $6,977.00
Desired Sum = $400,000
Time Period = 20 years or 240 months

Let monthly deposit be $x

$6,977.00*1.005^240 + $x*1.005^239 + $x*1.005^238 + ... + $x*1.005 + $x = $400,000
$6,977.00 * 1.005^240 + $x * (1.005^240 - 1) / 0.005 = $400,000
$7,013.55948 + $x * 462.040895 = $400,000
$x * 462.040895 = $392,986.44052
$x = $850.54

Monthly Deposit = $850.54

Answer c.

Total Amount Deposited = 60 * $100 + 240 * $850.54
Total Amount Deposited = $210,129.60

Interest Earned = Accumulated Sum - Total Amount Deposited
Interest Earned = $400,000 - $210,129.60
Interest Earned = $189,870.40