You are considering investing in a zero-coupon bond that sells for $250. At maturity in 16 years it will be redeemed for $1,000. What approximate annual rate of growth does this represent?
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A. B. C. D.B
The zero-coupon bond does not pay interest over its life, but it is sold at a discount to its face value and redeemed at its full face value at maturity. The return on investment in a zero-coupon bond is the difference between the purchase price and the redemption value, divided by the purchase price and expressed as an annual percentage rate (APR).
In this case, the zero-coupon bond is sold for $250 and will be redeemed for $1,000 in 16 years. The return on investment is the difference between the redemption value and the purchase price, which is $1,000 - $250 = $750. The time period for the investment is 16 years, so we need to calculate the APR that would make $250 grow to $1,000 over 16 years.
One way to do this is to use a financial calculator or a spreadsheet program to solve for the interest rate that makes the present value of the investment ($250) equal to the future value of the investment ($1,000) over a period of 16 years. Alternatively, we can use a formula to calculate the APR:
APR = (FV/PV)^(1/n) - 1
where FV is the future value, PV is the present value, n is the number of periods, and ^ means "to the power of".
Using this formula, we have:
APR = ($1,000/$250)^(1/16) - 1 = 1.0976 - 1 = 0.0976 or 9.76%
Therefore, the approximate annual rate of growth for this zero-coupon bond is 9%, which is closest to option B (9%).