Final answer:
When deciding between two payment streams, the time value of money must be considered. Paying $5,000 over 10 years is often more favorable due to the lower present value of future payments at a positive interest rate. Regarding bond valuation, as interest rates rise, the bond price tends to fall, leading to a purchase price below face value.
Step-by-step explanation:
If money is worth more than 0% per year to you, the decision between paying $10,000 per year for five years or paying $5,000 per year for 10 years involves understanding the time value of money. This economic principle suggests that a dollar today is worth more than a dollar in the future due to its potential earning capacity. To make an informed decision, one would need to consider the present value of these payment streams based on the opportunity cost of capital, or the expected rates of return that one could earn on investments over these time periods.
For example, if you could invest your money at a rate of 10% compounded annually, you'd need to understand how much $5,000 or $10,000 paid in the future would be worth today. This can be calculated using the formula for present value, which takes into account the interest rate and the number of periods. Generally, if the interest rate is positive, paying a smaller amount over a longer period (like $5,000 over 10 years) is often more advantageous because of the lower present value of those future payments.
If we were to apply the question of whether to pay more or less for a bond given a change in interest rates, the principle is similar. A bond's price will typically decrease as interest rates increase, so you would expect to pay less than the bond's face value, or less than $10,000 in the given scenario. This is because the bond's fixed interest payments are worth less in today's dollars when compared to the new higher interest rates available elsewhere.