You are considering purchasing a savings bond that will pay you $100 per year. The market...

You are considering purchasing a savings bond that will pay you $100 per year. The market interest rate currently is 5% per year.

(a) If this savings bond is a perpetuity (paying the same amount forever), what its price (or present value)?

(b) Suppose instead that the bond pays $100 per year for 20 years. What is its price in this case?

(c) The interest rate goes up, to 8% per year. What will happen to the price of the 20-year savings bond from part (b)? Explain how you reached your conclusion.

Solutions

Expert Solution

a) Present value = Cash flows Interest rate

Present value = $ 100 0.05

Present value = $ 2000

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b) Price = $ 100 (1+0.05)¹ + $ 100 (1+0.05)² + $ 100 (1+0.05)³ + $ 100 (1+0.05)⁴ + $ 100 (1+0.05)⁵ + $ 100 (1+0.05)⁶ + $ 100 (1+0.05)⁷ + $ 100 (1+0.05)⁸ + $ 100 (1+0.05)⁹ + $ 100 (1+0.05)¹⁰ + $ 100 (1+0.05)¹¹ + $ 100 (1+0.05)¹² + $ 100 (1+0.05)¹³ + $ 100 (1+0.05)¹⁴ + $ 100 (1+0.05)¹⁵ + $ 100 (1+0.05)¹⁶ + $ 100 (1+0.05)¹⁷ + $ 100 (1+0.05)¹⁸ + $ 100 (1+0.05)¹⁹ + $ 100 (1+0.05)²⁰

Price = $ 1246.22

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c) If interest rate goes up to 8% per year

Price = $ 100 (1+0.08)¹ + $ 100 (1+0.08)² + $ 100 (1+0.08)³ + $ 100 (1+0.08)⁴ + $ 100 (1+0.08)⁵ + $ 100 (1+0.08)⁶ + $ 100 (1+0.08)⁷ + $ 100 (1+0.08)⁸ + $ 100 (1+0.08)⁹ + $ 100 (1+0.08)¹⁰ + $ 100 (1+0.8)¹¹ + $ 100 (1+0.08)¹² + $ 100 (1+0.08)¹³ + $ 100 (1+0.08)¹⁴ + $ 100 (1+0.8)¹⁵ + $ 100 (1+0.08)¹⁶ + $ 100 (1+0.08)¹⁷ + $ 100 (1+0.08)¹⁸ + $ 100 (1+0.08)¹⁹ + $ 100 (1+0.08)²⁰

Price = $ 981.81

The price decreases when the interest rate goes up. The price and interest rates are inversely related to each other. When interest rate decreases, price increases and vice versa.

Rahul Sunny answered 1 year ago

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