Question

Think of four examples in your organization or from your personal life, or a combination of both, that demonstrate the following:

• Present Value (PV) of a lump sum
• Future Value (FV) of a lump sum
• Present Value (PV) of an annuity
• Future Value (FV) of an annuity

Explain your examples, including why they are relevant to your organization and/or personal life. Provide a rationale for interest or discount rates used in your examples.

Answer 1

1)	PV of a lump sum:
	An amount may be required in future, say 4 years from now, for
	meeting the down payment for buying a car. Supposing the
	amount required after 4 years is $5000 and the interest rate, with
	annual compounding, that can be earned is 10%, then the amount
	that I should deposit today is the PV of $5000.
	It is equal to 5000/1.10^4 = $3,415.07
	The interest rate here should be that which is promised by the bank
	where the deposit is made.
2)	FV of a lump sum:
	Suppose I lend $5000 to a friend who promises to repay it after
	2 years with interest at 5%, compounded annually, then the
	total amount that I will receive at the end of the 2nd year
	= 5000*1.05^2 = $5,512.50
	The interest rate is that which is agreed to between us.
3)	PV of an annuity:
	Suppose I can pay $500 per month towards a mortgage, then
	the maximum amount that I can get as a housing loan, is the PV
	of the monthly payments, which constitute an annuity. If the bank
	is charging 12% p.a (1% per month), then the amount of loan that'
	I can get, on a 30 year mortgage, is:
	= 500*(1.01^360-1)/(0.01*1.01^360) = $48,609.17
	The discount rate is the interest rate charged by the bank for the loan.
4)	FV of an annuity:
	If I can deposit $500 per month for the next 2 years for a vacation
	then the amount I would have at the end of 2 years is the FV of the
	annuity of 500. If the interest rate is 0.5% per month, the total
	amount that I will have = 500*(1.005^24-1)/0.005 = $12,715.98
	The interest rate is that which is promised by the bank.