Question

1.) Alexandria wants to receive $12,000 a year for 8 years. How much must Alexandria invest today in an annuity that pays 5% annually?

2.) Bill Jones plans to deposit $2100 at the end of every 6 months for the next 20 years into an annuity that pays 6%. What will be the value of Bill’s annuity at maturity?

3.) Johnson trucking company will have a $40,000 payment due in 5 years. How much would they need to invest quarterly in a fund paying 8%?

4.) Abby plans to deposit $100 at the end of every quarter for the next 10 years into an annuity that pays 6%. What will be the value of Abby’s annuity at maturity?

Answer 1

1]	The amount to be invested today is the PV of the annuity of $12,000 for 8 years at discounted at 5% = 12000*(1.05^8-1)/(0.05*1.05^8) =	$       77,558.55
2]	The FV of the annuity is to be found out = 2100*(1.03^40-1)/0.03 =	$ 1,58,342.65
	[It is 40 half years with half yearly interest of 3%]
3]	$40,000 is the FV of the quarterly deposits to be made.
	Hence, the required quarterly deposit = 40000*0.02/(1.02^20-1) =	$         1,646.27
	[it is 20 quarters with quarterly interest of 2%]
4]	FV of the annuity = 100*(1.015^40-1)/0.015 =	$         5,426.79
	[It is 40 quarters with quarterly interest of 1.5%]

ANSWERS WITH ROUNDING OF TO WHOLE DOLLARS:

1]	The amount to be invested today is the PV of the annuity of $12,000 for 8 years at discounted at 5% = 12000*(1.05^8-1)/(0.05*1.05^8) =	$             77,559
2]	The FV of the annuity is to be found out = 2100*(1.03^40-1)/0.03 =	$ 1,58,343
	[It is 40 half years with half yearly interest of 3%]
3]	$40,000 is the FV of the quarterly deposits to be made.
	Hence, the required quarterly deposit = 40000*0.02/(1.02^20-1) =	$               1,646
	[it is 20 quarters with quarterly interest of 2%]
4]	FV of the annuity = 100*(1.015^40-1)/0.015 =	$               5,427
	[It is 40 quarters with quarterly interest of 1.5%]