Question

You decide to invest $1,500 into a certificate of deposit (CD), which is a secure
bank investment option.
a) If you choose a bank advertising a certificate of deposit with 1.2% APR compounded
daily, how much money will be in this account at the end of 4 years?
b) If you choose a bank advertising a certificate of deposit with 1.2% APR compounded
monthly, how much money will be in this account at the end of 4 years?
c) Which CD option has more money in the account at the end of 4 years and explain
why?

Answer 1

a.
Value of money at the end of 4 years	=fv(rate,nper,pmt,pv)
	= $ 1,573.75
Where,
rate	=	1.2%/365	=	0.00003288
nper	=	4*365	=	1460
pmt			=	0
pv			=	$         -1,500
b.
Value of money at the end of 4 years	=fv(rate,nper,pmt,pv)
	= $ 1,573.72
Where,
rate	=	1.2%/12	=	0.00100
nper	=	4*12	=	48
pmt			=	0
pv			=	$         -1,500
c)
Daily compounding APR gives more money in 4 years.
Working:
Effective annual rate with daily compounding	=	((1+(i/n))^n)-1	Where,
	=	((1+(0.012/365))^365)-1	i	=	1.20%
	=	1.2072%		n	=	365
Effective annual rate with daily compounding	=	((1+(i/n))^n)-1	Where,
	=	((1+(0.012/12))^12)-1	i	=	1.20%
	=	1.2066%		n	=	12
As we can see that annual effective interest rate under daily compounding is more than monthly compounding.
So, Daily compounding has more money at the end of 4 years.