Yousaf, you need to compare how much John is going to pay under either alternative:

1) 3.2% simple interest rate. What John pays to borrow $500,000 for 3 years is equal to

$500,000*3.2%*3 = $48,000

2) 1.6% compound interest rate, compounded semi-annually.

Note that 1.6% is not the annual interest rate applied, but is already given to you as the compounded interest rate applied semi-annually. Otherwise it is clearly better to use option 2 as you pay half the interest rate than in option 1!

In this case, one pays interest rates every 6 months. More specifically, one pays 1.6% every 6 months. In a period of 3 years, there are 6 periods of 6 months each. So, John pays:

$500,000*[(1+1.6%)^{2*3 }-1] = $49,961.45.

The conclusion is that John is better off paying a simple interest rate as it pays less over the assigned period of 3 years.

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