Question

Springfield Learning sold zero coupon bonds (bonds that don't pay any interest, instead the bondholder gets just one payment, coming when the bond matures, from the issuer) and received $1,200 for each bond that will pay $20,000 when it matures in 35 years.

a. At what rate is Springfield Learning borrowing the money from investors?
b. If Nancy Muntz purchased a bond at the offering for $1,200 and sold it 15 years later for the market price of $3,400, what annual rate of return did she earn?
c. If Barney Gumble purchased Muntz's bond at the market price ($3,400) and held it 20 years until maturity, what annual rate of return would he have earned?

Answer 1

a. The rate at which Springfield Learning is borrowing the money from investors is approximately 5.46%.

b. Nancy Muntz earned an annual rate of return of approximately 5.22%.

c. Barney Gumble would have earned an annual rate of return of approximately 3.73%.

Step-by-step explanation:

a. Rate at which Springfield Learning borrowed the money (Yield to Maturity):

Formula used: YTM = (Face Value / Present Value)¹/ⁿ - 1, where n is the number of periods

Given:

Present Value (PV) = $1,200, Face Value (FV) = $20,000, n = 35 years

YTM = ($20,000 / $1,200)¹/³⁵ - 1

YTM ≈ 5.46%

Nancy Muntz's rate of return after 15 years:

Calculate the annual rate of return using the compound interest formula: ( A = P(1 + r)ⁿ), where A is the final amount, P is the principal amount, r is the annual interest rate, and n is the number of years.

Given:

Initial investment (P) = $1,200, Selling price (A) = $3,400, n = 15 years

Rearrange the formula to find the annual rate of return (r).

r = (A / P)¹/ⁿ - 1

r = ($3,400 / $1,200)¹/¹⁵ - 1

r ≈ 5.22%

Barney Gumble's rate of return if he holds the bond for 20 years until maturity:

Use the same compound interest formula as in part b, considering the time period until maturity.

Given:

Initial investment (P) = $3,400 (the market price), Face Value (A) = $20,000, n = 20 years

r = (A / P)¹/ⁿ - 1

r = ($20,000 / $3,400)¹/²° - 1

r ≈ 3.73%

These calculations showcase the application of financial formulas to assess borrowing rates, investment returns, and potential yields, enabling a clear understanding of profitability in zero-coupon bond investments for both Springfield Learning and individual investors like Nancy Muntz and Barney Gumble.