Question

Paul plans to contribute $150 at the end of every half year to an investment that earns 6% compounded monthly. If Paul starts contributing on his 41st birthday, how much will he accumulate by his 65th birthday?

Answer 1

By contributing $150 at the end of every half-year to an investment earning 6% compounded monthly from his 41st to 65th birthday, Paul will accumulate approximately $78,915.60.

Step-by-step explanation:

To calculate the future value of Paul's contributions, we can use the formula for compound interest:

`\[ FV = P \left(1 + (r)/(n)\right)^(nt) \]`

where:

- P is the periodic payment,

- r is the interest rate per period,

- n is the number of compounding periods per year, and

- t is the number of years.

In this case,
`\( P = $150 \), \( r = 6\% \)` or 0.06, n = 12 (monthly compounding), and
`\( t = (65 - 41) * 2 \)` (contributions every half-year from 41st to 65th birthday).

Plugging these values into the formula, we get:

`\[ FV = 150 \left(1 + (0.06)/(12)\right)^(12 * (65 - 41) * 2) \]`

Calculating this expression gives the final amount of approximately $78,915.60. This represents the total value of Paul's contributions and the compounded interest earned on those contributions over the specified period.

It's important to note that the success of such an investment strategy depends on the assumption that Paul consistently makes contributions as planned and the interest is compounded without interruption. Additionally, this calculation assumes no withdrawals or other adjustments to the investment during the specified period.