a zero - coupon bond is a bond that is sold now at a discount and will pay its face value at the time when…

a zero - coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made. a zero - coupon bond can be redeemed in 20 years for $10,000. how much should you be willing to pay for it now if you want the following returns? (a) 12% compounded monthly (b) 12% compounded continuously (a) for a return of 12% compounded monthly, you should pay $ (round to the nearest cent as needed.)

a zero - coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made. a zero - coupon bond can be redeemed in 20 years for $10,000. how much should you be willing to pay for it now if you want the following returns? (a) 12% compounded monthly (b) 12% compounded continuously (a) for a return of 12% compounded monthly, you should pay $ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the compound - interest formula for monthly compounding

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the future value, $P$ is the present value, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years. We want to find $P$, so we can rewrite the formula as $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$. Given $A=$10000$, $r = 0.12$, $n=12$ (compounded monthly), and $t = 20$.

Step2: Substitute the values into the formula

First, calculate the exponent $nt=12\times20 = 240$ and $\frac{r}{n}=\frac{0.12}{12}=0.01$. Then $(1+\frac{r}{n})^{nt}=(1 + 0.01)^{240}$. Using a calculator, $(1.01)^{240}\approx10.89255365$. Then $P=\frac{10000}{(1.01)^{240}}$.

Step3: Calculate the present - value

$P=\frac{10000}{10.89255365}\approx918.91$.

Answer:

$918.91$