Question

3) Ravi invests $10,000 in an investment account that pays 4% compounded semi- annually. Ravi takes each interest payment and invests it in a savings account that pays 1% compounded monthly. a) How much money does Ravi have at the end of 10 years? b) What is the effective annual rate he earned over 10 years?

Answer 1

	Analysis Of Question:
	In the question, it is given that Ravi takes every interest payment of investment
	and deposited it separately in saving account which gives Ravi 1% interest compounding monthly.
	Therefore we need to calculate the first effective semiannually rate of saving the account.
	Effective Semiannually Compounded interest rate
	Formula = (1+ i/n)^n -1
	Where,
	I = nominal interest rate
	n= Number of periods
	= (1+.02/12)^12 -1
	=1.0021%
	Now we need to calculate the annuity value of six-monthly interest at the end of 10 year
	F = P * ([1 + I]^N - 1 )/I
	Where,
	F = Future Value
	p= Periodical payment = $10000*4%/2=$200
	i= Interest rate = 1.0021/2=0.050105%
	N = Number of periods =10 years *2 = 20
	=[$200(1.0.000501)^20-1]0.000501
	=$4019.10
a)	Therefore Ravi would have at the end of 10 year
	=$4019.10+$10000
	=$14019.1
b)	Affective Annual Rate He Earned Over 10 Years
	=$4019.1/10000 *1/10
	=4.0191%