Question

Annual percentage yield (APY) is 2.25% that is compounded daily. What is the total amount of interest at the end of 5 years ?

Answer 1

Here in the question we are give Annual Percentage Yield (APY) that is compounded daily. We need to first calculate the Annaul Percentage Rate (APR) and then we can calculate the interst at the end of 5 years
APR	=	n[(1+APY)1/n-1]
	Here
	n= No. of compounding periods = 365
	APY = Annual Percentage Yield = 2.25% = .0225
APR	=	365[(1+0.0225)1/365--1]
APR	=	365[(1.0225)1/365--1]
APR	=	365[1.0000610-1]
APR	=	365*0.0000610
APR	=	0.022251
APR	or say	2.2251%
Interest amount for 5 Years
Interest	=	P[(1+APR)n]-P             n
	Here
	P = Principal Amount (Assuming $ 1 here)
	n= compounding periods = 365 days
	APR = Annual Percentage Rate = 2.2251% = .02251
	t = Time (No. of compounding periods = 365 days*5 years = 1825 days
Interest	=	P[(1+APR)t] -P             n
	=	1[(1+0.02251)182]-1           365
	=	1[(1+0.02251)1825]-1             365
	=	1[(1.000060962)1825]-1
	=	1.1177-1
	=	$0.1177