Question

which of the following saving plans do you prefer? A. 8% compound daily, B. 8.5% compound quarterly, C. 9% compounded semi-annually, or D. 9.5% compounded annually.

Answer 1

Effective Rate = [( 1+r)^n ] - 1

WHere r is int rate per period & n is no. of compoundings per anum

A: Compounded daily

Daily int rate = 0.08 / 365

= 0.000219

Effective rate = [ ( 1+0.000219)^365 ] - 1

= [ ( 1.000219)^365 ] - 1

= 1.0833 - 1

0.0833 i.e 8.33%

B: Compounded Quarterly

Quarterly int rate = 0.085 / 4

= 0.02125

Effective rate = [ ( 1+0.02125)^4 ] - 1

= [ ( 1.02125)^4 ] - 1

= 1.0877 - 1

0.0877 i.e 8.77%

C: Compounded Semi Annually

Half Yearly int rate = 0.09 / 2

= 0.045

Effective rate = [ ( 1+0.045)^2 ] - 1

= [ ( 1.045)^2 ] - 1

= 1.092 - 1

0.092 i.e 9.20%

D: Annual Compoundinf

Effective Rate is 9.5%

OPtion D is having more effective rate per anum, Hence 9.5% compounding plan is suggested.

Please comment, if any further assistance is required.