Question

Determine which is the better investment 3.99% compounded semi annually Lee 3.8% compounded quarterly round your answer 2 decimal places

Answer 1

Remember that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

In the 3.99% compounded semiannually

we have

r=3.99%=0.0399

n=2

substitute

`\begin{gathered} A=P(1+(0.0399)/(2))^(2t) \\ \\ A=P(1.01995)^(2t) \end{gathered}`

and

`\begin{gathered} A=P[(1.01995)^2]^t \\ A=P(1.0403)^t \end{gathered}`

the rate is r=1.0403-1=0.0403=4.03%

In the 3.8% compounded quarterly

we have

r=3.8%=0.038

n=4

substitute

`\begin{gathered} A=P(1+(0.038)/(4))^(2t) \\ A=P(1.0095)^(2t) \\ A=P[(1.0095)^2]^t \\ A=P(1.0191)^t \end{gathered}`

the rate is r=1.0191-1=0.0191=1.91%

therefore

the 3.99% compounded semiannually is a better investment