Question

Determine which is the better investment: 4.57% compounded daily or 4.62% compounded quarterly. Round your answers to 2 decimal places.

The 4.57% daily investment gives an effective rate of ____ %.
The 4.62% quarterly investment gives an effective rate of ____%.
Therefore, the _____ Investment is a better investment.

Answer 1

To determine the better investment between 4.57% compounded daily and 4.62% compounded quarterly, you calculate the effective annual rate (EAR) for each using the compound interest formula. By substituting the appropriate values into the formula and comparing the results, you can conclude which investment yields a higher return.

Step-by-step explanation:

To determine which investment is better when comparing 4.57% compounded daily with 4.62% compounded quarterly, we must calculate the effective annual rate (EAR) for each. The formula for EAR is (1 + r/n)^(n*t) - 1, where r is the annual nominal interest rate, n is the number of compounding periods per year, and t is the time in years.

For the daily compounding:

1. The nominal interest rate (r) is 4.57% or 0.0457.
2. The compounding periods per year (n) for daily compounding is 365.
3. Time (t) is 1 year.

EAR for daily compounding = ((1 + 0.0457/365)^(365*1)) - 1, which, when calculated and rounded to two decimal places, gives an EAR of approximately ____%.

For the quarterly compounding:

1. The nominal interest rate (r) is 4.62% or 0.0462.
2. The compounding periods per year (n) for quarterly compounding is 4.
3. Time (t) is 1 year.

EAR for quarterly compounding = ((1 + 0.0462/4)^(4*1)) - 1, which, when calculated and rounded to two decimal places, gives an EAR of approximately ____%.

Comparing the two EARs calculated will determine which investment is better. The investment with the higher effective annual rate provides the better return and is therefore the better option.