I am a beginner to finance, today I found a question looks very simple that I am not quite sure about it.

Question: Given I am paid \$50,000 now, growing at $6\%$ per year for a total of 10 years, but the discount rate is $4\%$, solve for the present value.

My thought is first calculating the nominal value in 10 years, which is $50000 \times (1+0.06)^{10}$, then discount this value using $4\%$ to get the present value.

Is there anything wrong with my idea? Thanks.


The proper way is to discount each and every single item of cash flow (the initial $50,000 "grant" as well as the 10 individual interest payments) each one at the discount rate of 4%.

In numbers, it's quite a big difference between the two methods, as shown in this table:

Expected return rate

If you discounted just the ending capital - as suggested by you - you would erroneously conclude the NPV as $60,491.63, as shown in red.

However, if you discount each and every cash flow item, the initial inflow of USD 50,000 as well as each interest payment, the NPV will show as $81,474.88

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