Question

Gordon wants to buy a bond that will mature to $5000 in 6 years. How much did he pay for the bond now if it earns interest at a rate at 2.5% per year, compounded continuously? Do not round any intermediate computations and round your answer to the nearest cent.

Answer 1

The amount of money A in an account after t years of investing a principal P at a rate r compounded continuously, is:

`A=Pe^(rt)`

To find the value P that he must pay now so that the amount of money will be equal to $5000 in 6 years at a rate of 2.5% per year, isolate P and substitute A=5000, r=2.5/100 and t=6:

`\begin{gathered} \Rightarrow P=(A)/(e^(rt))=Ae^(-rt) \\ \Rightarrow P=5000\cdot e^{-(2.5)/(100)*6} \\ =5000\cdot e^(-0.025*6) \\ =5000\cdot e^(-0.15) \\ =4303.53988\ldots \\ \approx4303.54 \end{gathered}`

Therefore, he paid $4303.54.