Question

QUESTION 5 Linda inherited a sum of $50,000 from one of her grandparents. She would like to wisely invest the inheritance in one of the following three investment opportunities available for a period of 10 years. Help choose the best investment opportunity for Linda. 1.8% compounded quarterly. ii. 8.90% compounded daily. ii. 8.95% compounded monthly iv. 8.9% compounded continuously.

Answer 1

Calculating Effective Annual Rate(EAR) for each of the option to determine best Investment Opportunity:-

i) 8% compounded Quarterly

$EAR = (1+\frac{r}{m})^m-1$

where, r = Interest rate = 8%

m = No of times compounding in a year = 4

$EAR = (1+\frac{0.08}{4})^4-1$

EAR = 1.082432 - 1

EAR = 8.2432%

ii) 8.90% compounded Daily

$EAR = (1+\frac{r}{m})^m-1$

where, r = Interest rate = 8.90%

m = No of times compounding in a year = 365

$EAR = (1+\frac{0.0890}{365})^{365}-1$

EAR = 1.093069 - 1

EAR = 9.3069%

iii) 8.95% compounded Monthly

$EAR = (1+\frac{r}{m})^m-1$

where, r = Interest rate = 8.90%

m = No of times compounding in a year = 12

$EAR = (1+\frac{0.0895}{12})^{12}-1$

EAR = 1.093264 - 1

EAR = 9.3264%

iv) 8.90% compounded Continously

where, r = Interest rate = 8%

EAR = 1.093081 - 1

EAR = 9.3081%

As EAR of 8.95% componded Monthly is highest among the other Options, it is better to choose OPTION III.