Question

One year before maturity, the price of a bond with a principal amount of $1,000 and a coupon rate of 2 percent paid annually fell to $981. The new one-year interest rate must be

Answer 1

7%.

One-year interest rate (R) = [C + (F - P) / N] / [(F + P) / 2], where

C: Annual coupon = $1,000 x 5% = $50,

F: Face value = $1,000,

P: Market price = $981,

N: Years left to maturity = 1

So,

R = [50 + (1,000 - 981) / 1] / [(1,000 + 981) / 2]

= [50 + 19] / (1,981 / 2)

= 69 / 990.5

= 0.07

= 7%.

The principal is the money that you originally agreed to pay back. Interest is the cost of borrowing the principal. Generally, any payment made on an auto loan will be applied first to any fees that are due (for example, late fees).

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