Using the R script, answer the following questions. Please show all works for full credit.

1. In Chapter 7 of our course materials, you have learned about how to value a bond.

Bond Price = jQuery224014640883224393075_1601668397272? ?_jQuery22409155548702643563_1601668501884?? (1 + ?) ? ? ?=1 + ??? (1 + ?) ? , where ???: par value of the bond ?_????: annual coupon rate ?: time to maturity ?: bond yield Now, you have to find coupon rate when we know all other variables, such as the bond price, par value, time to maturity, and yield.

In order to find coupon rate instead of bond price, you can use the following formula (if you solve the equation above for ?_????, you can easily obtain this formula). c_rate = ???? ????? ??? (1 + ?) ? ??? (1 + ?) ? ? ?=1

Suppose you are investing in a bond that has $1,157.449 of current bond price, $1,200 of par value, 4 years to maturity, and 5% of yield (discount rate). So, I have written these codes to calculate coupon rate for you.

# Create time t t <- seq(1, 4, 1)

# Create present value factor pv_factor <- 1 / (1 + 0.05)^t

# Current bond price bond_value <- 1157.449

# Par value c_rate <- (1157.449 - 1200 / (1+0.05)^4) / (1200*sum(pv_factor)) c_rate

[1] 0.0400001

Referring to the codes above, create a function to calculate coupon rate. Complete the body of the following function (bond_value: current bond price, par: par value, ttm: time to maturity, and y: yield).

c_rate <- function (bond_value, par, ttm, y) { body of work here}

The answers should be as follows:

c_rate(1091.5946, 1000, 5, 0.03) [1] 0.0500001

c_rate(1000, 973.9658, 3, 0.06) [1] 0.06999999

c_rate(1500, 1661.355, 15, 0.06) [1] 0.05