Question

Determine which is the better investment 4.29% compound daily or 4.42% compounded quarterly round your answer to 2 decimal places

Answer 1

Effective interest rate is given by the next formula:

`r=(1+(i)/(n))\placeholder{⬚}^n-1`

r is the effective interest rate

i is the interest rate (in decimals)

n is the number of times the interest is compound per year

For the given investments:

1. 4.29% compound daily

`\begin{gathered} i=0.0429 \\ n=365 \\ \\ r=(1+(0.0429)/(365))\placeholder{⬚}^(365)-1 \\ \\ r=0.04383 \end{gathered}`

Multiply by 100 to get it in %:

`0.04383*100=4.38`

The 4.29% daily investment gives an effective rate of 4.38%

2. 4.42% compounded quarterly

`\begin{gathered} i=0.0442 \\ n=4 \\ \\ r=(1+(0.0442)/(4))\placeholder{⬚}^4-1 \\ \\ r=0.04493 \end{gathered}`

Multiply by 100 to get it in %:

`0.04493*100=4.49`

The 4.42% quarterly investment gives an effective rate of 4.49%

Therefore, the 4.42% quarterly investment is a better investment