Question

Determine which is the better investment: 7.56% compounded semiannually or 7.53% compounded quarterly, found your answers co 2 deamul ploces.

The 7.56 % semiancual investment gives an effective rate of ____ %.
The 7.53 % quarterly investment qives an effective rate of _____ %.
Therefore, The ___ investment is a better investment.

Answer 1

The 7.53% compounded quarterly provides a higher effective annual rate (EAR) of 7.72% compared to the 7.56% compounded semiannually which gives an EAR of 7.60%. Therefore, the quarterly investment is the better of the two.

Step-by-step explanation:

To determine which investment is better, we calculate the effective annual rate (EAR) for both. The formula for EAR is (1 + r/n)nt - 1, where r is the nominal interest rate, n is the number of compounding periods per year, and t is the time in years.

For the 7.56% compounded semiannually, we have r = 0.0756 and n = 2 (since it's semiannually). The EAR is calculated as:

(1 + 0.0756/2)2×1 - 1 = (1 + 0.0378)2 - 1 = 1.0759944 - 1 = 0.0759944 or 7.60% (rounded to two decimal places).

For the 7.53% compounded quarterly, we have r = 0.0753 and n = 4 (since it's quarterly). The EAR is:

(1 + 0.0753/4)4×1 - 1 = (1 + 0.018825)4 - 1 = 1.0772216 - 1 = 0.0772216 or 7.72% (rounded to two decimal places).

Therefore, the quarterly investment gives a higher effective rate and is the better investment