In investment account pays interest at the rate
of per year, compounded semi annually What
the amount that should be depasited now so
hat can be withdrawn at the end of every
ix months for the next ten years?

To solve this problem, we need to determine the present value of an annuity that allows you to withdraw every six months for ten years, with a 5% annual interest rate compounded semi-annually. The semi-annual interest rate is . This means that over the ten-year term, you will make a total of withdrawals (one every six months).

Using the Present Value of Annuity formula:

Where:

Substituting in the values:

Calculating this gives you the amount that needs to be deposited today to enable those withdrawals.

Now, to engage with some fun and pertinent insights:

Before getting into the nitty-gritty of investment accounts, did you know that the concept of compounding was famously described by Albert Einstein as the “eighth wonder of the world”? This means that the earlier you start saving, the more your money can grow over time, thanks to earning “interest on interest” — talk about a magical trick!

For those looking to optimize their investments, a common mistake is to underestimate the impact of small, regular contributions versus a lump sum. By regularly investing smaller amounts, not only do you take advantage of dollar-cost averaging which helps mitigate volatility, but you also train yourself to save consistently—setting yourself up for a financial windfall in your future!