Question

which one of the following provides the greatest annual interest?

a) 10% compounded annualy

b) 9.9% compounded monthly

c) 9.8% compounded weekly

d) 9.6% compounded daily

please elaborate on how to find it.

Thankss

Answer 1

As the stated interest rates compound at different intervels, they are converted into effective annual interest rates for comparison to evaluate which one gives highest annual interest.

a- 10% annual compounding

	Effective annual interest rate=	(1+periodic interest rate)^m   -1
rs=	Stated interest rate	10%
	compounding frequency	Once in 12 months
m	number of periods	1
rs/m	period interest rate	10.0000%
	Effective annual interest rate=	(1+0.1)^1    -1
	Effective annual interest rate=	10.0000%

When compounding is once in a year, stated rate equals effective annual interest. Thus, EAR is 10%.

b - 9.9% monthly compouding

	Effective annual interest rate=	(1+periodic interest rate)^m   -1
rs=	Stated interest rate	9.9%
	compounding frequency	Once in 1 months
m	number of periods	12
rs/m	period interest rate	0.8250%
	Effective annual interest rate=	(1+0.00825)^12    -1
	Effective annual interest rate=	10.3618%

EAR is 10.36%

c - 9.8% weekly

	Effective annual interest rate=	(1+periodic interest rate)^m   -1
rs=	Stated interest rate	9.80%
	compounding frequency	weekly
m	number of periods	52
rs/m	period interest rate	0.1885%
	Effective annual interest rate=	(1+0.001885)^52    -1
	Effective annual interest rate=	10.2861%

d - 9.6% daily

	Effective annual interest rate=	(1+periodic interest rate)^m   -1
rs=	Stated interest rate	9.60%
	compounding frequency	weekly
m	number of periods	365
rs/m	period interest rate	0.0263%
	Effective annual interest rate=	(1+0.000263)^365    -1
	Effective annual interest rate=	10.0745%

Thus of the given options 9.9% monthly compounding provides highest annual interest.