Question

Trey purchased a 30-year Zero-Coupon bond. It has a value of $20,000.00 at maturity and is offered at 5.5% interest compounded semiannually. How much will he need to invest to buy this bond?

a. $4000.45
b. $3727.54
c. $4221.55
d. $3927.54

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 20000\\ P=\textit{original amount deposited}\\ r=rate\to 5.5\%\to (5.5)/(100)\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &30 \end{cases}`

`20000 = P\left(1+(0.055)/(2)\right)^(2\cdot 30) \implies 20000=P(1.0275)^(60) \\\\\\ \cfrac{20000}{(1.0275)^(60)}=P\implies 3927.54\approx P`