To pay for college, you have just taken out a 1,000...

To pay for college, you have just taken out a $\$ 1,000$ government loan that makes you pay $\$ 126$ per year for 25 years. However, you dont have to start making these payments until you graduate from college two years from now. Why is the yield to maturity necessarily less than $12 \%$ (this is the yield to maturity on a normal $\$ 1,000$ fixed-payment loan in which you pay $\$ 126$ per year for $25 \text { years }) ?$

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Key Concepts

Yield to Maturity

Yield to maturity (YTM) is the internal rate of return on a fixed-income security or loan, calculated by equating the present value of all expected future cash flows (such as regular payments and the final principal repayment) to the amount received upfront. It represents the annualized return an investor would earn if the instrument were held until maturity, taking into account the timing and size of all cash flows.

Time Value of Money

The time value of money principle is central to finance and states that a dollar today is worth more than a dollar in the future due to its potential earning capacity. This concept underpins how future cash flows are discounted to the present value, meaning that the timing of payments has a direct effect on their current worth.

Deferred Cash Flows

When cash flows are deferred, as in the case where payments begin later than the origination of the loan, the present value of those cash flows is lower because there is an extended period over which these future amounts are discounted back to the present. This delay means that for the same nominal payment amounts, the effective yield (or rate of return) is reduced compared to a scenario where payments commence immediately.

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